Internal problem ID [11003]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number: Problem 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {t^{2} y^{\prime \prime }+3 y^{\prime } t +y-t^{7}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(t^2*diff(y(t),t$2)+3*t*diff(y(t),t)+y(t)=t^7,y(t), singsol=all)
\[ y \left (t \right ) = \frac {c_{2}}{t}+\frac {t^{7}}{64}+\frac {c_{1} \ln \left (t \right )}{t} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 26
DSolve[t^2*y''[t]+3*t*y'[t]+y[t]==t^7,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {t^8+64 c_2 \log (t)+64 c_1}{64 t} \\ \end{align*}