76.17.14 problem 23

Internal problem ID [17700]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 11:01:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 31

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

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