91Ó°ÊÓ

Solve the following equations using the method of undetermined coefficients. $$y^{\prime \prime}+y=3 \sin 2 x+x \cos 2 x$$

Solve the following equations using the method of undetermined coefficients. $$y^{\prime \prime}+3 y^{\prime}-28 y=10 e^{-5 x}$$

Solve the following equations using the method of undetermined coefficients. $$y^{\prime \prime}+10 y^{\prime}+25 y=x e^{-5 x}+4$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$y^{\prime \prime}-y^{\prime}-y=x+e^{-x}$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$y^{\prime \prime}-3 y=x^{2}-4 x+11$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$y^{\prime \prime}-y^{\prime}-4 y=e^{x} \cos 3 x$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$2 y^{\prime \prime}-y^{\prime}+y=\left(x^{2}-5 x\right) e^{-x}$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$4 y^{\prime \prime}+5 y^{\prime}-2 y=e^{2 x}+x \sin x$$

In each of the following problems, a. Write the form for the particular solution \(y_{p}(x)\) for the method of undetermined coefficients. b. \([\mathrm{T}]\) Use a computer algebra system to find a particular solution to the given equation. $$y^{\prime \prime}-y^{\prime}-2 y=x^{2} e^{x} \sin x$$

Solve the differential equation using either the method of undetermined coefficients or the variation of parameters. $$y^{\prime \prime}+3 y^{\prime}-4 y=2 e^{x}$$