76.17.13 problem 22

Internal problem ID [17699]
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 : 22
Date solved : Tuesday, January 28, 2025 at 11:01:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=2 t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

dsolve(t^2*diff(y(t),t$2)-t*(t+2)*diff(y(t),t)+(t+2)*y(t)=2*t^3,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 20

DSolve[t^2*D[y[t],{t,2}]-t*(t+2)*D[y[t],t]+(t+2)*y[t]==2*t^3,y[t],t,IncludeSingularSolutions -> True]
 

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