Internal problem ID [11500]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.4.2 Variation of parameters.
Exercises page 124
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {t^{2} x^{\prime \prime }-2 x=t^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(t^2*diff(x(t),t$2)-2*x(t)=t^3,x(t), singsol=all)
\[ x \left (t \right ) = c_{2} t^{2}+\frac {t^{3}}{4}+\frac {c_{1}}{t} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 25
DSolve[t^2*x''[t]-2*x[t]==t^3,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^3}{4}+c_2 t^2+\frac {c_1}{t} \]