Internal problem ID [7578]
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]]
\[ \boxed {2 x^{2} y^{\prime \prime }+x \left (x +5\right ) y^{\prime }-\left (2-3 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
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)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, {\mathrm e}^{-\frac {x}{2}}+c_{2} \sqrt {x}\, {\mathrm e}^{-\frac {x}{2}} \left (\int \frac {{\mathrm e}^{\frac {x}{2}}}{x^{\frac {7}{2}}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.23 (sec). Leaf size: 70
DSolve[2*x^2*y''[x]+x*(5+x)*y'[x]-(2-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{15} \left (-\frac {2 c_2 \left (x^2+x+3\right )}{x^2}+15 c_1 e^{-x/2} \sqrt {x}+\sqrt {2} c_2 e^{-x/2} \sqrt {-x} \Gamma \left (\frac {1}{2},-\frac {x}{2}\right )\right ) \]