Internal problem ID [695]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-2 y-3 t^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(t^2*diff(y(t),t$2)-2*y(t) = 3*t^2-1,y(t), singsol=all)
\[ y \relax (t ) = t^{2} c_{2}+\frac {1}{2}+\frac {c_{1}}{t}+t^{2} \ln \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 31
DSolve[t^2*y''[t]-2*y[t] == 3*t^2-1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^2 \log (t)+\left (-\frac {1}{3}+c_2\right ) t^2+\frac {c_1}{t}+\frac {1}{2} \\ \end{align*}