Internal problem ID [6831]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 99.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.099 (sec). Leaf size: 22
dsolve(2*x^2*(2+3*x)*diff(y(x),x$2)+x*(4+11*x)*diff(y(x),x)-(1-x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} \left (3 x +2\right )^{\frac {1}{6}}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 32
DSolve[2*x^2*(2+3*x)*y''[x]+x*(4+11*x)*y'[x]-(1-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \sqrt [6]{6 x+4}+2^{5/6} c_1}{\sqrt {x}} \\ \end{align*}