Internal problem ID [11504]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} x^{\prime \prime }-3 x^{\prime } t +3 x=4 t^{7}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(t^2*diff(x(t),t$2)-3*t*diff(x(t),t)+3*x(t)=4*t^7,x(t), singsol=all)
\[ x \left (t \right ) = \left (\frac {1}{6} t^{6}+\frac {1}{2} c_{1} t^{2}+c_{2} \right ) t \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 23
DSolve[t^2*x''[t]-3*t*x'[t]+3*x[t]==4*t^7,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^7}{6}+c_2 t^3+c_1 t \]