Internal problem ID [13784]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x -9 y=12 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=12*x^3,y(x), singsol=all)
\[ y \left (x \right ) = \frac {6 x^{6} \ln \left (x \right )+\left (3 c_{1} -1\right ) x^{6}+3 c_{2}}{3 x^{3}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 29
DSolve[x^2*y''[x]+x*y'[x]-9*y[x]==12*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^3 \log (x)+\left (-\frac {1}{3}+c_2\right ) x^3+\frac {c_1}{x^3} \]