Internal problem ID [1757]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-t \,{\mathrm e}^{3 t}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=t*exp(3*t)+1,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{2 t}+\frac {1}{2}-\frac {3 \,{\mathrm e}^{3 t}}{4}+\frac {{\mathrm e}^{3 t} t}{2}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 37
DSolve[y''[t]-3*y'[t]+2*y[t]==t*Exp[3*t]+1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} e^{3 t} (2 t-3)+c_1 e^t+c_2 e^{2 t}+\frac {1}{2} \\ \end{align*}