Internal problem ID [4345]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y-2 x^{3}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=2*x^3,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{3}+x^{3} \ln \left (x \right ) c_{1} +\ln \left (x \right )^{2} x^{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 22
DSolve[x^2*y''[x]-5*x*y'[x]+9*y[x]==2*x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^3 \left (\log ^2(x)+3 c_2 \log (x)+c_1\right ) \\ \end{align*}