Internal problem ID [1756]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }-3 y^{\prime }+y-\left (t^{2}+1\right ) {\mathrm e}^{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 39
dsolve(2*diff(y(t),t$2)-3*diff(y(t),t)+y(t)=(t^2+1)*exp(t),y(t), singsol=all)
\[ y \relax (t ) = 2 c_{1} {\mathrm e}^{t}+\frac {{\mathrm e}^{t} t^{3}}{3}-2 \,{\mathrm e}^{t} t^{2}+9 t \,{\mathrm e}^{t}-18 \,{\mathrm e}^{t}+c_{2} {\mathrm e}^{\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 36
DSolve[2*y''[t]-3*y'[t]+y[t]==(t^2+1)*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 e^{t/2}+e^t \left (\frac {1}{3} t ((t-6) t+27)-18+c_2\right ) \\ \end{align*}