Find a particular solution for ?^2?′′ + ??′ − 4? = ?^3 Given the fact that...

Find a particular solution for

?^2?′′ + ??′ − 4? = ?^3

Given the fact that the general homogeneous solution is ??(?) = ?1(?^2) + ?2t(?^−2)

Expert Solution

The complementary solution of the differential equation be

??(?) = ?1(?^2) + ?2 (?^−2).

In the form of particular solution, we take the coefficient of t^2 as 0, because t^2 is already present in the general homogeneous solution.

please give a thumbs up if you are benefited.

Colby Messinger answered 1 year ago

Find the particular solution to ?″+16?=−24sec(4?) Do not include the complementary solution ??=?1?1+?2?2.

Find a particular solution of the given differential equation. Use a CAS as an aid in...

Find a particular solution of the given differential equation. Use a CAS as an aid in carrying out differentiations, simplifications, and algebra. y(4) + 2y'' + y = 11 cos(x) − 12x sin(x)

Use the method of variation of parameters to find a particular solution of the given differential...

Use the method of variation of parameters to find a particular solution of the given differential equation and then find the general solution of the ODE. y'' + y = tan(t)

(D^(2)+2D+5)^(2)(D-3)^(3)y=xe^(3x)-5e^(x)sin(2x) Find the homogeneous solution. Find a particular solution. Finding of coefficients is not necessary.

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

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!

.1. a.) By inspection, find a particular solution of 2?′′ − 5? = 13 b.) By...

.1. a.) By inspection, find a particular solution of 2?′′ − 5? = 13 b.) By inspection, find a particular solution of 2?′′−5?= −27? c.) Find a particular solution of 2?′′−5?= −27?+13 d.) Find a particular solution of 19,378.47?′′+35? = 6−56?

Find a particular solution to the differential equation: y'' - 1y' - 20y = -400t^3

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and...

4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the point corresponding to ? = 1. (b) Find the equation of the osculating plane at the point corresponding to ? = 1. (c) Find the equation of the normal plane at the point corresponding to ? = 1

In Exercises 7–29 use variation of parameters to find a particular solution, given the solutions y1,...

In Exercises 7–29 use variation of parameters to find a particular solution, given the solutions y1, y2 of the complementary equation. 1.) 4xy'' + 2y' + y = sin sqrt(x); y1 = cos sqrt(x), y2 = sin sqrt(x) 2.) x^2y''− 2xy' + (x^2 + 2)y = x^3 cos x; y1 = x cos x, y2 = x sinx Please help!!! with explanation thank you very much only these two excersices from homework.

Question