Internal problem ID [7419]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 700.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(x^2*diff(y(x),x$2)+(x+2*x^2)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (2 x^{2}-4 x +3\right )}{x^{2}}+\frac {c_{2} {\mathrm e}^{-2 x} \left (2 x +3\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 42
DSolve[x^2*y''[x]+(x+2*x^2)*y'[x]-4*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\frac {c_1 e^{-2 x} (4 x+6)+c_2 (3-4 x)}{x^2}+2 (-1+c_2)\right ) \\ \end{align*}