14.10.9 problem 9

Internal problem ID [2591]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.4. The method of variation of parameters. Excercises page 156
Problem number : 9
Date solved : Monday, January 27, 2025 at 06:01:32 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-2 y&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

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

\[ y = c_2 \,t^{2}+\frac {t^{2} \ln \left (t \right )}{3}+\frac {c_1}{t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 34

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

\[ y(t)\to \frac {3 t^3 \log (t)+(-1+9 c_2) t^3+9 c_1}{9 t} \]