1. Solve the equation (D² + D – 2)y = 2x – 40 cos 2x.

Q: T/2 cos(9t) cos(18t) dt

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Q: 5. Find : 60 y= (b) y = cos (11x³ + 5x). dx

A: SOLUTION-

Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2ex sin2(x/2)

A: Given the given differential equation is d2ydx2-2dydx+4y=2exsin2x2

Q: dx2 16y = 10 cos 4x

A:

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 1 (D2 – 3D+ 2) Y = cos²(e-²)

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Q: y' + 2y = 3 sin(e2×)

A: y.e^(2x)=-3/2 cos(e^(2x)) + k

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: 37/2 8 cos x dx T/2

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Q: D- y" + 2y' + 5y = 6e2* + x sin? x + e*cos 2x %3D

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Q: (a) /4 1+3 cos² 1 d.x; COST dx3B

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Q: Find the general solution of the equation: y' -2y = 2 sin(3t).

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Q: 3. Solve the DE dy = x + 2x %3D a. dx 3 dy b. dx %3D dy C. -= 4 cos 6x %3D dx

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Q: 4) y-3y'+2y =e"(1+ cos 2x).

A: First we find out C.F. and then we find out P.I. and then the complete solution is y=C.F.+P.I.

Q: Find a particular solution yp for the equation. y" - 6y' + 5y = cos3x 3sin3x

A: Consider a non-homogeneous differential equation of the form a(x)y''+b(x)y'+c(x)y=r(x). Then the…

Q: y(x) =- 10 n +2x' +8x' + 48) +qe* +c, sin(x)+ c, cos(x)

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Q: Solve the given DE. (D² – 3D + 2) Y 1 cos² (e¬²)

A: Differential equations, method of variation of perameters

Q: y''''+8y'''+32y''+64y'+39y=e^(-2x)((4-15x)cos3x-(4+15x)sin3x) Find a particular equation for:

A: The given differential equation is: y''''+8y'''+32y''+64y'+39y=e-2x ((4-15x) cos3x-(4+15x) sin3x)…

Q: d²y Solve the following DE : dy + 2 dx + y = cos²x dx2

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Q: -2 | (t2 + 3) cos(5t)dt 0.

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Q: *10. cos Z = 0.5234 YX _ y 24

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Q: 1 y Solve the integral: cos -dy dx - T/2 Jo

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Q: #+2 Q.23) cos²3x dx = 24 a)- #+24 KT -24

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Q: solve for the ganeral solution.  y' + x-1y = cos(x2)

A: Find the general solution.

Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: d²x dt.² +2 d'y (1² - y = = cos 21. 2 da 9=0

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Q: d²y 9. +y= sin 3x cos 2x 2

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Q: y" – 4y' + 13y = e2x cos 3x -

A: Differential equations

Q: 5. (y" – y) = e-X cos(3x) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Ex: SOLVE THE D.E. y"+ 2y' + 2y = e-*/cos3x

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Q: 4. (D² – 3D+ 2) y = 14 sin 2x – 18 cos 2x -

A: From the given differential equation; D2-3D+2y=14sin2x-18cos2x So, the auxiliary equation is:…

Q: cos(2t + 号) dt = e2t-3 寸 ト す

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Q: f(t) = e¯3t cos ( at + cos ( 2at + 3 2

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Q: Solve the equation: dy (4x + 5)2 1 tan x · Y = 2 ,3 dx 2 cos x

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Q: Find the complete solution of d2y/dx2 + 2dy/dx + y = sin x cos 2x.

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Q: What is the solution of D.E (D2 - 2D)y = e sinx when solved using the method of undetermined

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Q: S' SE x² cos(xy)dxdy

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Q: Q6// Solve the equation: y cos2 x dy + sin x dx = 0.

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Q: 1- y" - 6y' - 7y 2 cos Dt sin Mt Find Particular solution

A: It can be solved by finding C.F. and P.I

Q: Find a particular equation for: y(4) + 8y''' + 32y'' + 64y' + 39y = e-2x[(4 - 15x) cos 3x - (4 +…

A: The given equation can be written as, y4+8y3+32y2+64y1+39y=e-2x4-15xcos3x-4+15xsin3x it is also can…

Q: 4. Solve for in the equations below: dx a) -1 dy y? dx b) cos x – sin y 2 = 2- 3 ) xe+ e = 3"

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Q: 9. y = logs (e cos(2x))

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Q: y" + 9y = e" cos 3x + x² + x³e*

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Q: e. y"-3y'-4y = -8e' cos 2t

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Q: (e) y' +2y : = cos(2x)

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Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

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Q: e/ (cos(2²) + y²) dæ + (sin(y²) + 2aæ²) dy Evaluate

A: In this question, we need to find the integral over C.  C is a closed curve with the boundary are…