10.10.22 problem 32

Internal problem ID [1354]
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
Date solved : Monday, January 27, 2025 at 04:52:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y&=2 \left (t -1\right ) {\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 39

dsolve((1-t)*diff(y(t),t$2)+t*diff(y(t),t)-y(t) = 2*(t-1)*exp(-t),y(t), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (-1+t \right ) t +2 \,\operatorname {Ei}_{1}\left (-2+2 t \right ) {\mathrm e}^{t -2}+{\mathrm e}^{t} c_1 +c_2 t +{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.220 (sec). Leaf size: 47

DSolve[(1-t)*D[y[t],{t,2}]+t*D[y[t],t]-y[t] ==2*(t-1)*Exp[-t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -2 e^{t-2} \operatorname {ExpIntegralEi}(2-2 t)+\frac {2 t \operatorname {ExpIntegralEi}(1-t)}{e}+e^{-t}+c_1 e^t-c_2 t \]