10.10.15 problem 15

Internal problem ID [1347]
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 : 15
Date solved : Monday, January 27, 2025 at 04:51:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.008 (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)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 31

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

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