1. Determine the form of a particular solution for the following differential equations. (Do not evaluate...

1. Determine the form of a particular solution for the following differential equations. (Do not evaluate the coefficients.)

(a) y'' − y' − 6y = x^2 e^x sin x + (2x^3 − 1)e ^ cos x.

(b) y'' − y' − 6y = (2 − 3x^3 )e^3x .

(c) y'' + 4y' + 4y = x(e^x + e^−x )^2 .

(d) y'' − 2y' + 2y = (x − 1)e^x sin x + x^2 e^−x cos x.

2. Find a general solution to the differential equation y'' − 3y' + 2y = x^2 + 1 − x sin x + xe^2x

Expert Solution

Colby Messinger answered 1 year ago

Determine the form of a particular solution to the following differential equations (do not evaluate coefficients)....

Determine the form of a particular solution to the following differential equations (do not evaluate coefficients). (a)y′′ −4y′ = x+1+ xe^(2x) + e^(4x) + e^(4x)sin4x

Determine the reasonable form of the particular solution for each non homogeneous differential equation. Do not...

Determine the reasonable form of the particular solution for each non homogeneous differential equation. Do not solve it. a) y''-y'-2y= e^-x+xcos2x+e^xsin2x. b) D^2[y] +4y =1+x^2+xsin2x.

Set up the appropriate form of the particular solution to each of the differential equations below,...

Set up the appropriate form of the particular solution to each of the differential equations below, but do NOT determine the values of the coefficients. (a) y′′ +10y′ +25y=2e^(5t) +te^(−5t) b) y′′ +9y=5t^2 +4cos(3t)+6e^(3t)

Find the general solution of the following differential equations (complementary function + particular solution). Find the...

Find the general solution of the following differential equations (complementary function + particular solution). Find the particular solution by inspection or by (6.18), (6.23), or (6.24). Also find a computer solution and reconcile differences if necessary, noticing especially whether the particular solution is in simplest form [see (6.26) and the discussion after (6.15)]. (D2+2D+17)y = 60e−4x sin 5x

For each of the following differential equations, find the particular solution that satisfies the additional given...

For each of the following differential equations, find the particular solution that satisfies the additional given property (called an initial condition). y'y = x + 1

a) Determine the correct form of the particular solution

a) Determine the correct form of the particular solution y" + y = sin x b) Solve IVP: y" + y = e^x + x^3; y(0) = 2, y'(0) = 0 c) Solve IVP: y" + y' -2y = x + sin 2x; y(0) = 1, y'(0) = 0

Determine the general solution of the differential equations. Write out the solution ? explicitly as a...

Determine the general solution of the differential equations. Write out the solution ? explicitly as a function of ?. (a) 3?^2?^2 ??/?? = 2?−1 (b) 2 ??/?? + 3? = ?^−2? − 5

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" +...

Using variation of parameters, find a particular solution of the given differential equations: a.) 2y" + 3y' - 2y = 25e-2t (answer should be: y(t) = 2e-2t (2e5/2 t - 5t - 2) b.) y" - 2y' + 2y = 6 (answer should be: y = 3 + (-3cos(t) + 3sin(t))et ) Please show work!

Determine the general solution to the differential equations using the method of variation of parameters y''...

Determine the general solution to the differential equations using the method of variation of parameters y'' + 6y'+9y = x^(-1)

Use the annihilator method to write the form of the particular solution but do not solve...

Use the annihilator method to write the form of the particular solution but do not solve the differential equation 1. y”+y=e^(-x)+x^2 2. y”’+y=xe^(2x)cosx+sinx Find the general solution 1. y”-2y’-8y=4e^(2x)-21e^(-3x) Find the general solution of the given differential equation. Then find the solution that passes through the given initial solution 1. y”+6y+10y=3xe^(-3x)-2e^(3x)cosx, y(0)=1, y’(0)=-2

Question