Internal problem ID [704]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (-t +1\right ) y^{\prime \prime }+t y^{\prime }-y-2 \,{\mathrm e}^{-t} \left (t -1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 46
dsolve((1-t)*diff(y(t),t$2)+t*diff(y(t),t)-y(t) = 2*(t-1)*exp(-t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} t +c_{1} {\mathrm e}^{t}-2 \,{\mathrm e}^{-t} \left ({\mathrm e}^{t -1} \expIntegral \left (1, t -1\right ) t -{\mathrm e}^{2 t -2} \expIntegral \left (1, 2 t -2\right )-\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 47
DSolve[(1-t)*y''[t]+t*y'[t]-y[t] ==2*(t-1)*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -2 e^{t-2} \text {Ei}(2-2 t)+\frac {2 t \text {Ei}(1-t)}{e}+e^{-t}+c_1 e^t-c_2 t \\ \end{align*}