Internal problem ID [6822]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 90.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve(2*x^2*diff(y(x),x$2)+x*(5+x)*diff(y(x),x)-(2-3*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, {\mathrm e}^{-\frac {x}{2}}+\frac {c_{2} \left (i {\mathrm e}^{-\frac {x}{2}} x^{\frac {5}{2}} \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {i \sqrt {2}\, \sqrt {x}}{2}\right )+2 x^{2}+2 x +6\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 59
DSolve[2*x^2*y''[x]+x*(5+x)*y'[x]-(2-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{15} c_2 e^{-x/2} x E_{\frac {1}{2}}\left (-\frac {x}{2}\right )-\frac {2 c_2 \left (x^2+x+3\right )}{15 x^2}+c_1 e^{-x/2} \sqrt {x} \\ \end{align*}