Internal problem ID [6854]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 122.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 33
dsolve(4*x^2*(3+2*x+x^2)*diff(y(x),x$2)-x*(3-14*x-15*x^2)*diff(y(x),x)+(3+7*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x}{x^{2}+2 x +3}+\frac {c_{2} x^{\frac {1}{4}}}{x^{2}+2 x +3} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 31
DSolve[4*x^2*(3+2*x+x^2)*y''[x]-x*(3-14*x-15*x^2)*y'[x]+(3+7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 \sqrt [4]{x}+4 c_2 x}{3 x (x+2)+9} \\ \end{align*}