10.10.16 problem 16

Internal problem ID [1348]
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 : 16
Date solved : Monday, January 27, 2025 at 04:51:56 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 )^{2} {\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 25

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

\[ y = c_2 t +{\mathrm e}^{t} c_1 -t \,{\mathrm e}^{-t}+\frac {{\mathrm e}^{-t}}{2} \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 30

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

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