Problem 4
Use the method of variation of parameters to determine the general solution of
the given differential equation.
$$
y^{\prime \prime \prime}+y^{\prime}=\sec t, \quad-\pi / 2
Problem 5
Use the method of variation of parameters to determine the general solution of the given differential equation. $$ y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=e^{-t} \sin t $$
Problem 5
Express the given complex number in the form \(R(\cos \theta+\) \(i \sin \theta)=R e^{i \theta}\) $$ \sqrt{3}-i $$
Problem 5
Determine the general solution of the given differential equation. \(y^{\mathrm{iv}}-4 y^{\prime \prime}=t^{2}+e^{t}\)
Problem 6
Use the method of variation of parameters to determine the general solution of the given differential equation. $$ y^{\mathrm{iv}}+2 y^{\prime \prime}+y=\sin t $$
Problem 6
Determine the general solution of the given differential equation. \(y^{\mathrm{iv}}+2 y^{\prime \prime}+y=3+\cos 2 t\)
Problem 6
determine intervals in which solutions are sure to exist. $$ \left(x^{2}-4\right) y^{\mathrm{vi}}+x^{2} y^{\prime \prime \prime}+9 y=0 $$
Problem 6
Express the given complex number in the form \(R(\cos \theta+\) \(i \sin \theta)=R e^{i \theta}\) $$ -1-i $$
Problem 7
determine whether the given set of functions is linearly dependent or linearly independent. If they are linearly dependent, find a linear relation among them. $$ f_{1}(t)=2 t-3, \quad f_{2}(t)=t^{2}+1, \quad f_{3}(t)=2 t^{2}-t $$
Problem 7
Find the general solution of the given differential equation. Leave your
answer in terms of one or more integrals.
$$
y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=\sec t, \quad-\pi /
2
