Internal problem ID [13455]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.15 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y=6 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=6*x^3,y(x), singsol=all)
\[ y = c_{2} x^{3}+\ln \left (x \right ) x^{3} c_{1} +3 \ln \left (x \right )^{2} x^{3} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 24
DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==6*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3 \left (3 \log ^2(x)+3 c_2 \log (x)+c_1\right ) \]