Internal problem ID [701]
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: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y-4 t^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 22
dsolve(t^2*diff(y(t),t$2)-2*t*diff(y(t),t)+2*y(t) = 4*t^2,y(t), singsol=all)
\[ y \relax (t ) = t^{2} c_{2}+c_{1} t +4 t^{2} \left (\ln \relax (t )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 21
DSolve[t^2*y''[t]-2*t*y'[t]+2*y[t] ==4*t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t (4 t \log (t)+(-4+c_2) t+c_1) \\ \end{align*}