Find a general solution. Show the details of your work [3] yi = y1 + Y2 + 10 cos t y2 = 3y1 – y2 – 10 sin t

Q: 3. f(t) = 2e3t sin 2t – 3e3t cos 2t -

A:

Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

A:

Q: Find a particular solution to y" + 16y = -16 sin(4t). Yp ||

A:

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: se the method of undetermined coefficients to find the general solution to: y'' + y = 5 Cos(t)

A: Use the method of undermined coefficient to find the general solutionof differential equationy''+y=5…

Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x…

Q: Find the particular solution : y" + y" +4y sin2x sin2x (b) Yp =sin2x (a) yp = - (c) Yp =- cos2x ()…

A:

Q: y = c, e2* cos 3x+C, e²* sin 3x

A:

Q: 1. f(t) = -e-3t sin 4t + 3

A: L { sinat } = as2+ a2 , L { eat f (t) } = F ( s- a) where  F (s)  is Laplace transformation of f(t)L…

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: 8. Find a particular solution yp(x) to the equation y" +y' – 2y = 5 sin x in the form yp(x) = c1…

A:

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

A:

Q: 2. Evaluate (x2 – 1)e" dx T/2 3. Evaluate cos (0) d0. Write your ans"

A: Consider the integral- I=∫01(x2-1)exdx =∫01x2exdx-∫01exdxLet I=I1-I2—(1)Where ,I1=∫01x2exdx and…

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

A:

Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

A:

Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

A:

Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

A:

Q: 4. Find the general solution of wt Wra + sin(x +t) by using the coordinate method.

A: As mentionsed solving question 4 Given: wtt=wxx + sin (x+t)

Q: ý(t) + 100 y(t) = 15 cos 5t + 20 sin 5t, y(0) = 25, ý(t)= 0 V138388 [ y(t) = - Q1 = 2n – tan cos…

A: Given that y''(t)+100y(t)=15cos5t+20sin5t, y(0)=25,y(t)=0 Take the homogenous equation,…

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

A:

Q: 5. ) Using the Method of Undetermined Coefficients, give an appropriate guess for y,. y(4) + 9y" =…

A:

Q: y" + 9y = e" cos 3x + x² + x³e*

A: 1f(D)eaxX = eax1f(D+a)X 1f(D)eax = 1f(a)eax 1f(D2)cos ax = 1f(-a2) cos ax

Q: Q1: Use the Improved Euler method to find y' = cos2x + sin3x ,0<x < 1,y(0) = 1, with h = 0.25. %3D…

A:

Q: Q7// find the general solution 1 (sin-ix + =y)dx + sec-1xdy = 0 xVx² – 1

A:

Q: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

A:

Q: (cos t)y" + (sin t)y' – ty = 0,

A:

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

A:

Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

Q: (b) Apply the method of undetermined coefficients to find a particular solution y, of 3y" + y – 2y =…

A:

Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

A:

Q: 5. Find (b) y = cos (11xs+ 5x).

A:

Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

Q: Q/ Find the generd solution of the differention equation y"-3y'-2y=4 cos (x) +2 sin (x)

A:

Q: V 3 (d) r(1/6 + At) - r(n/6) = 3 COS At sin At cos At + SV3 sin At it

A:

Q: 8. (D² + 100)y = -300 %3D a. y = C, cos 10x + C2x sin 10x - 3 %3D b. y = C1 cos 10x + C2 sin 10x- 3…

A: Solution: (D2 +100)y =-300 The Auxiliary equation is m2+100 =0 m2 = -100 m= 10i , -10i

Q: Find the general solution of: y"-3y 8e* + sin 2-

A:

Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

A:

Q: 2T d) f(x)=5 sin (x+1)+2 e) f(x) = -2 cos 2(x+ 1) + 1_ 17. Find the rule of the sinusoi

A:

Q: Q1 / Find the solution to the following IVP. 1 cos-1 yý – (2 cos x* sin x – 1) + (sin x)y = 0, y(A)…

A:

Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: Use any appropriate method to find the general solution of each of the following equations. dy sin 2…

A:

Q: Use imaginary part of the solution to the complexified version of the following ODE to find its…

A:

Q: evaluate the triple iterated integral.

A:

Q: y" + 25y = 10 sin(5t). Yp =

A:

Q: 8. Find a particular solution y,(x) to the equation y" +y – 2y = 5 sin r - in the form yp(x) = c1…

A:

Q: (a) y" + 3y' – 2y = -e2" (5 cos 2r + 9 sin 2a)

A:

Q: Find the general solution using the method of undetermined coefficients. y'' + 3y' - 2y = -e(2x) (5…

A: It is given that y\'\' + 3y\' – 2y = –e(2x) (5 cos 2x + 9 sin 2x)        …… (1)Consider y\'\' + 3y\'…

Q: z"- 4z'+5z = x sin3x- cos3x %3D

A: We first find the complementary solution  of the given differential equation by finding the roots of…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.