76.17.19 problem 28

Internal problem ID [17705]
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 : 28
Date solved : Tuesday, January 28, 2025 at 11:01:33 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} t^{2} y^{\prime \prime }-2 y&=3 t^{2}-1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(t^2*diff(y(t),t$2)-2*y(t)=3*t^2-1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 31

DSolve[t^2*D[y[t],{t,2}]-2*y[t]==3*t^2-1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2 \log (t)+\left (-\frac {1}{3}+c_2\right ) t^2+\frac {c_1}{t}+\frac {1}{2} \]