Internal problem ID [9392]
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]]
\[ \boxed {y^{\prime \prime }+x^{4} y^{\prime }-y x^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(diff(diff(y(x),x),x)+x^4*diff(y(x),x)-x^3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {9 \,{\mathrm e}^{-\frac {x^{5}}{5}} \left (\frac {25 c_{2} x^{5} \operatorname {WhittakerM}\left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right ) {\mathrm e}^{\frac {x^{5}}{10}}}{9}+\frac {25 c_{1} x^{3} {\mathrm e}^{\frac {x^{5}}{5}}}{9}+5^{\frac {3}{5}} c_{2} \left (x^{5}\right )^{\frac {2}{5}} \left (x^{5}+4\right )\right )}{25 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 39
DSolve[-(x^3*y[x]) + x^4*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-\frac {c_2 \sqrt [5]{x^5} \Gamma \left (-\frac {1}{5},\frac {x^5}{5}\right )}{5 \sqrt [5]{5}} \]