Internal problem ID [7748]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 261.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(x^2*diff(y(x),x$2)+(x+2*x^2)*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (2 x^{2}-4 x +3\right )}{x^{2}}+\frac {c_{2} {\mathrm e}^{-2 x} \left (2 x +3\right )}{2 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.362 (sec). Leaf size: 44
DSolve[x^2*y''[x]+(x+2*x^2)*y'[x]-4*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (\frac {2 c_1 e^{-2 x} (2 x+3)}{x^2}+\frac {c_2 \left (2 x^2-4 x+3\right )}{x^2}-2\right ) \]