1.766 problem 783

Internal problem ID [7500]

Book: Collection of Kovacic problems
Section: section 1
Problem number: 783.
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^{2}+y x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 43

dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} x +c_{2} \left (6 \,3^{\frac {2}{3}} \left (\Gamma \left (\frac {2}{3}\right )-\Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )\right ) \left (-x^{3}\right )^{\frac {1}{3}}+18 \,{\mathrm e}^{\frac {x^{3}}{3}}\right ) \]

Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 27

DSolve[y''[x]-x^2*y'[x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x-\frac {1}{3} c_2 E_{\frac {4}{3}}\left (-\frac {x^3}{3}\right ) \\ \end{align*}