(a) By inspection, find a particular solution of y" + 2y = 18. Yp(x) (b) By inspection, find a particular solution of y" + 2y = -12x. Yp(x) %3D (c) Find a particular solution of y" + 2y = -12x + 18. YpCx) = (d) Find a particular solution of y" + 2y = 24x + 9. Yp(x) = ||

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

A:

Q: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: For the difference equation given by y(k +2) - y(k + 1) + 2y(k) = 2* with y(1) = y(0) = 0 Find the…

A:

Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

Q: Show the solution using methods of undetermined coefficient. The answer should be Y = C1et + C2…

A:

Q: Find the general solution x²y" - xy + y = x lnx

A:

Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

A:

Q: Differentiate y = 2sin? (x³) + 3x and evaluate y (0). Enter the value y (0) in the box and upload…

A:

Q: Let 1 2 -1 A = 2 4 -2 -2 Describe all solutions of A = 0. * = x2 +x3 +x4

A:

Q: Find the general solution of y" = x-1 A. y = xln x – C1x + C2 B.y = xln x – C1x - C2 C.y = xln x +…

A:

Q: In(-/-) (vi) 2x In - x = 0

A:

Q: y" – 2y' + y = -3 – x + x?.

A:

Q: (3) y "'- 2y "– 4y '+8y = 6xe²* %3D

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: -1 -1 3. Find a particular solution of x' = -2 2 x+ 4 -1 -2 et

A:

Q: 7. −ydx + (x + √xy)dy = 0

A:

Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

Q: Which of the following is the general solution of x 2 V) 2 -xy'-56x 2 =0? O a.…

A: We have to solve given problem: Note: given differential equations is wrong. According to options…

Q: 6. Find the positive number that when multiplied by 15 is equal to its square subtracted from 34.

A:

Q: 2 Find the general Solution of yty = 2xcosx -CosX %3D

A:

Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…

Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x

Q: 4 Solve for y(x) y"-y-16=0

A:

Q: 3) y +2/u

A: Given: y+2y=x

Q: 5. Solve the equation xydx + (x + 1)dy = 0. ex = cy(x + 1) yex = c(x + 1) c. y = cex(x + 1) d. ye*(x…

A: