Internal problem ID [703]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y-{\mathrm e}^{2 t} t^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 23
dsolve(t*diff(y(t),t$2)-(1+t)*diff(y(t),t)+y(t) = t^2*exp(2*t),y(t), singsol=all)
\[ y \relax (t ) = \left (t +1\right ) c_{2}+c_{1} {\mathrm e}^{t}+\frac {\left (t -1\right ) {\mathrm e}^{2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 31
DSolve[t*y''[t]-(1+t)*y'[t]+y[t] ==t^2*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} e^{2 t} (t-1)+c_1 e^t-c_2 (t+1) \\ \end{align*}