Internal problem ID [8639]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1059.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } x^{4}-y x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(diff(y(x),x),x)+x^4*diff(y(x),x)-x^3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\frac {c_{2} {\mathrm e}^{-\frac {x^{5}}{10}} \left (x^{10} \WhittakerM \left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )+\left (9 x^{5}+36\right ) \WhittakerM \left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )\right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 27
DSolve[-(x^3*y[x]) + x^4*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x-\frac {1}{5} c_2 E_{\frac {6}{5}}\left (\frac {x^5}{5}\right ) \\ \end{align*}