giải bài toán cao cấp

Solver will continue anyway.. Solver will continue anyway.. Solver will continue anyway.. Solver will continue anyway... Solver will continue anyway.. Solver will continue anyway.. Solve

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NV1.Tính các tích phân xác định trong bài 9.1 với cận num đến num+10

Error in integrate(f, lower = 166, upper = 176) :

non-finite function value

In addition: Warning message:

In sqrt((1 - x^2)^3) : NaNs produced

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In addition: Warning message:

In log(tan(x)) : NaNs produced

11,dx

> f<-function(x){(x^2-1)/(x^4+1)}

> integrate(f,lower=166,upper=176)

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the integral is probably divergent

non-finite function value

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2.003271e-06 with absolute error < 2.2e-20

NV2 Tính đạo hàm cấp 1 & 2 các hàm số trong bài 12.2 1) Z=

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y^2 * (2 * y) + (x^3 + y^3) * 2)/(x^2 + y^2)^2 - (x^3 + y^3) * (2 * y) * (2 * (2 * y * (x^2 + y^2)))/((x^2 + y^2)^2)^2)

(x^2 + y^2)^-0.5)) * (1 + 0.5 * (2 * x * (x^2 + y^2)^-0.5))/(x + sqrt(x^2 + y^2))^2

3) Z=

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exp(atan(y/x)) * (1/x/(1 + (y/x)^2)) * (1/x/(1 + (y/x)^2)) -

exp(atan(y/x)) * (1/x * (2 * (1/x * (y/x)))/(1 + (y/x)^2)^2)

4) Z= ln

Đạo hàm cấp 1 x

> D(expression(log((sqrt(x^2+y^2)-x)/(sqrt(x^2+y^2)+x))),'x')((0.5 * (2 * x * (x^2 + y^2)^-0.5) - 1)/(sqrt(x^2 + y^2) + x) - (sqrt(x^2 + y^2) - x) * (0.5 * (2 * x * (x^2 + y^2)^-0.5) +

1)/(sqrt(x^2 + y^2) + x)^2)/((sqrt(x^2 + y^2) - x)/(sqrt(x^2 + y^2) + x))

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(0.5 * (2 * (x^2 + y^2)^-0.5 + 2 * x * (-0.5 * (2 * x * (x^2 +

y^2)^-1.5)))/(sqrt(x^2 + y^2) + x) - (0.5 * (2 * x * (x^2 +

y^2)^-0.5) - 1) * (0.5 * (2 * x * (x^2 + y^2)^-0.5) + 1)/(sqrt(x^2 + y^2) + x)^2 - (((0.5 * (2 * x * (x^2 + y^2)^-0.5) - 1) *

(0.5 * (2 * x * (x^2 + y^2)^-0.5) + 1) + (sqrt(x^2 + y^2) -

x) * (0.5 * (2 * (x^2 + y^2)^-0.5 + 2 * x * (-0.5 * (2 *

x * (x^2 + y^2)^-1.5)))))/(sqrt(x^2 + y^2) + x)^2 - (sqrt(x^2 + y^2) - x) * (0.5 * (2 * x * (x^2 + y^2)^-0.5) + 1) * (2 *

((0.5 * (2 * x * (x^2 + y^2)^-0.5) + 1) * (sqrt(x^2 + y^2) +

x)))/((sqrt(x^2 + y^2) + x)^2)^2))/((sqrt(x^2 + y^2) -

x)/(sqrt(x^2 + y^2) + x)) - ((0.5 * (2 * x * (x^2 + y^2)^-0.5) - 1)/(sqrt(x^2 + y^2) + x) - (sqrt(x^2 + y^2) - x) * (0.5 *

(2 * x * (x^2 + y^2)^-0.5) + 1)/(sqrt(x^2 + y^2) + x)^2) *

((0.5 * (2 * x * (x^2 + y^2)^-0.5) - 1)/(sqrt(x^2 + y^2) +

x) - (sqrt(x^2 + y^2) - x) * (0.5 * (2 * x * (x^2 + y^2)^-0.5) + 1)/(sqrt(x^2 + y^2) + x)^2)/((sqrt(x^2 + y^2) - x)/(sqrt(x^2 + y^2) + x))^2

Đạo hàm cấp 1 y

> D(expression(log((sqrt(x^2+y^2)-x)/(sqrt(x^2+y^2)+x))),'y')(0.5 * (2 * y * (x^2 + y^2)^-0.5)/(sqrt(x^2 + y^2) + x) - (sqrt(x^2 + y^2) - x) * (0.5 * (2 * y * (x^2 + y^2)^-0.5))/(sqrt(x^2 +

y^2) + x)^2)/((sqrt(x^2 + y^2) - x)/(sqrt(x^2 + y^2) + x))

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y^2)^-0.5)) * (2 * (0.5 * (2 * x * (x^2 + y^2)^-0.5) *

(sqrt(x^2 + y^2))))/((sqrt(x^2 + y^2))^2)^2))/(1 + ((sqrt(x^2 -

y^2))/(sqrt(x^2 + y^2)))^2) - (0.5 * (2 * x * (x^2 - y^2)^-0.5)/(sqrt(x^2 + y^2)) - (sqrt(x^2 - y^2)) * (0.5 * (2 * x * (x^2 + y^2)^-0.5))/(sqrt(x^2 + y^2))^2) * (2 * ((0.5 * (2 * x * (x^2 - y^2)^-0.5)/(sqrt(x^2 +

y^2)) - (sqrt(x^2 - y^2)) * (0.5 * (2 * x * (x^2 + y^2)^-0.5))/(sqrt(x^2 + y^2))^2) * ((sqrt(x^2 - y^2))/(sqrt(x^2 + y^2)))))/(1 + ((sqrt(x^2 -

y^2)^-0.5)) * (2 * (0.5 * (2 * y * (x^2 + y^2)^-0.5) *

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y^2))/(sqrt(x^2 + y^2)))^2) + (0.5 * (2 * y * (x^2 - y^2)^-0.5)/(sqrt(x^2 + y^2)) + (sqrt(x^2 - y^2)) * (0.5 * (2 * y * (x^2 + y^2)^-0.5))/(sqrt(x^2 + y^2))^2) * (2 * ((0.5 * (2 * y * (x^2 - y^2)^-0.5)/(sqrt(x^2 +

y^2)) + (sqrt(x^2 - y^2)) * (0.5 * (2 * y * (x^2 + y^2)^-0.5))/(sqrt(x^2 + y^2))^2) * ((sqrt(x^2 - y^2))/(sqrt(x^2 + y^2)))))/(1 + ((sqrt(x^2 -

y^2))/(sqrt(x^2 + y^2)))^2)^2)

7) Z=

> D(expression((x+y)^(sin(x)*sin(y))),'x')

(x + y)^((sin(x) * sin(y)) - 1) * (sin(x) * sin(y)) + (x + y)^(sin(x) *

sin(y)) * (log((x + y)) * (cos(x) * sin(y)))

> D( D(expression((x+y)^(sin(x)*sin(y))),'x'),'x')

((x + y)^(((sin(x) * sin(y)) - 1) - 1) * ((sin(x) * sin(y)) -

1) + (x + y)^((sin(x) * sin(y)) - 1) * (log((x + y)) * (cos(x) *

sin(y)))) * (sin(x) * sin(y)) + (x + y)^((sin(x) * sin(y)) -

1) * (cos(x) * sin(y)) + (((x + y)^((sin(x) * sin(y)) - 1) *

(sin(x) * sin(y)) + (x + y)^(sin(x) * sin(y)) * (log((x +

y)) * (cos(x) * sin(y)))) * (log((x + y)) * (cos(x) * sin(y))) +

(x + y)^(sin(x) * sin(y)) * (1/(x + y) * (cos(x) * sin(y)) -

log((x + y)) * (sin(x) * sin(y))))

Đạo hàm cấp 1 y

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> D(expression((x+y)^(sin(x)*sin(y))),'y')

(x + y)^((sin(x) * sin(y)) - 1) * (sin(x) * sin(y)) + (x + y)^(sin(x) *

sin(y)) * (log((x + y)) * (sin(x) * cos(y)))

Đạo hàm cấp 2 y

> D( D(expression((x+y)^(sin(x)*sin(y))),'y'),'y')

((x + y)^(((sin(x) * sin(y)) - 1) - 1) * ((sin(x) * sin(y)) -

1) + (x + y)^((sin(x) * sin(y)) - 1) * (log((x + y)) * (sin(x) *

cos(y)))) * (sin(x) * sin(y)) + (x + y)^((sin(x) * sin(y)) -

1) * (sin(x) * cos(y)) + (((x + y)^((sin(x) * sin(y)) - 1) *

(sin(x) * sin(y)) + (x + y)^(sin(x) * sin(y)) * (log((x +

y)) * (sin(x) * cos(y)))) * (log((x + y)) * (sin(x) * cos(y))) +

(x + y)^(sin(x) * sin(y)) * (1/(x + y) * (sin(x) * cos(y)) -

log((x + y)) * (sin(x) * sin(y))))

NV3 Vẽ đồ thị nghiệm riêng của các PTVP trong bài 10.4 với điều kiện ban đầu y(num)

= 2 trên miền [num, num+10]

1

2 2

2

'

y x

xy y

−

=

> ham <- function (x, y,parms) {list(c((2*x)/(1+x^2)))}

> dieukien <- c(y = 2)

> nghiem <- ode(y = dieukien, func = ham,times = 166:176, parms = 0)

> plot(nghiem, type = "l", which = "y",lwd = 2, xlab = "Truc x", ylab = "Truc y",main =

"PTVP")

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"PTVP")

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"PTVP")

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4 y'−y.sinx=sinxcosx

> ham <- function (x, y,parms) {list(c(y*sin(x)+sin(x)*cos(x)))}

"PTVP")

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2: In asin(x) : NaNs produced

6 ' 2 ( )

2 y x x

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Error in lsoda(y, times, func, parms, ) :

illegal input detected before taking any integration steps - see written message

7

2

22

xy− =

> ham <- function (x, y,parms) {list(c((2*y)/x+2*x^3))}

"PTVP")

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1: In sqrt(1 - x^2) : NaNs produced2: In asin(x) : NaNs produced

3: In sqrt(1 - x^2) : NaNs produced4: In sqrt(1 - x^2) : NaNs produced5: In asin(x) : NaNs produced

6: In sqrt(1 - x^2) : NaNs produced7: In sqrt(1 - x^2) : NaNs produced8: In asin(x) : NaNs produced

9: In sqrt(1 - x^2) : NaNs produced10: In sqrt(1 - x^2) : NaNs produced11: In asin(x) : NaNs produced12: In sqrt(1 - x^2) : NaNs produced13: In sqrt(1 - x^2) : NaNs produced14: In asin(x) : NaNs produced15: In sqrt(1 - x^2) : NaNs produced16: In sqrt(1 - x^2) : NaNs produced17: In asin(x) : NaNs produced18: In sqrt(1 - x^2) : NaNs produced19: In sqrt(1 - x^2) : NaNs produced20: In asin(x) : NaNs produced21: In sqrt(1 - x^2) : NaNs produced22: In sqrt(1 - x^2) : NaNs produced23: In asin(x) : NaNs produced

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x x

y

y− =

2 0

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> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2")

DLSODA- Warning Internal T (=R1) and H (=R2) are

such that in the machine, T + H = T on the next step

(H = step size) Solver will continue anyway

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T not in interval TCUR - HU (= R1) to TCUR (=R2)

In above message, R1 = 168, R2 = 168

DLSODA- Trouble in DINTDY ITASK = I1, TOUT = R1

In above message, I1 = 1

In above message, R1 = 170

> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP cấp 2") Error in plot(nghiem, type = "l", which = "y1", lwd = 2, ylab = "Truc y", :

object 'nghiem' not found

3) ) 4y” – 20y’ + 25y = 0

> library(deSolve)

> ham <- function (x, y,parms) {list(c(4*y[2], 20*y[2]-25*y[1]))}

> dieukien <- c(y1 = 2, y2 = 1)

*Đồ thị

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> library(deSolve)

> ham <- function (x, y,parms) {list(c(y[2], 4*y[1]-12*x^2-6*x-4))}

> dieukien <- c(y1 = 2, y2 = 1)

> plot(nghiem, type = "l", which = "y1",lwd = 2, ylab = "Truc y",main = "PTVP

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6) y” – 5y’ + 4y = 4

> library(deSolve)

> ham <- function (x, y,parms) {list(c(y[2], 5 * y[2] - 4 * y[1] + 4 * x^2 * exp(1)^x))}

> dieukien <- c(y1 = 2, y2 = 1)

In above message, R1 = 168, R2 = 1.93588e-81

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such that in the machine, T + H = T on the next step (H = step size) Solver will continue anyway.

DLSODA- Warning Internal T (=R1) and H (=R2) are such that in the machine, T + H = T on the next step (H = step size) Solver will continue anyway

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DLSODA- Warning Internal T (=R1) and H (=R2) are such that in the machine, T + H = T on the next step (H = step size) Solver will continue anyway.

DLSODA- Above warning has been issued I1 times

It will not be issued again for this problem

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*Đồ thị

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DLSODA- Warning Internal T (=R1) and H (=R2) are such that in the machine, T + H = T on the next step (H = step size) Solver will continue anyway.

DLSODA- Warning Internal T (=R1) and H (=R2) are such that in the machine, T + H = T on the next step

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(H = step size) Solver will continue anyway.

DLSODA- Above warning has been issued I1 times

It will not be issued again for this problem

*Đồ thị

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