Internal problem ID [702]
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: 30.
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 }+7 t y^{\prime }+5 y-t=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(t^2*diff(y(t),t$2)+7*t*diff(y(t),t)+5*y(t) = t,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{2}+\frac {2 \left (c_{1}+\frac {t^{2}}{2}\right )^{3}}{3}-c_{1} \left (c_{1}+\frac {t^{2}}{2}\right )^{2}}{t^{5}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 23
DSolve[t^2*y''[t]+7*t*y'[t]+5*y[t] ==t,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_1}{t^5}+\frac {t}{12}+\frac {c_2}{t} \\ \end{align*}