Internal problem ID [14731]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = x^{3} \left (c_{2} +c_{1} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 27
DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^3 \left (\log ^2(x)+6 c_2 \log (x)+2 c_1\right ) \]