Internal problem ID [10314]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60.
Exact equation. Integrating factor. Page 139
Problem number: Ex 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^5*diff(y(x),x$2)+(2*x^4-x)*diff(y(x),x)-(2*x^3-1)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} x \,{\mathrm e}^{-\frac {1}{3 x^{3}}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 22
DSolve[x^5*y''[x]+(2*x^4-x)*y'[x]-(2*x^3-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (c_2 e^{-\frac {1}{3 x^3}}+c_1\right ) \\ \end{align*}