10.10.13 problem 13

Internal problem ID [1345]
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 : 13
Date solved : Monday, January 27, 2025 at 04:51:51 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: 0.001 (sec). Leaf size: 22

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

\[ y = c_2 \,t^{2}+\frac {1}{2}+t^{2} \ln \left (t \right )+\frac {c_1}{t} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 31

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

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