Internal problem ID [6909]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 177.
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 (2 x +1\right ) y^{\prime \prime }-2 x \left (-x +4\right ) y^{\prime }-\left (7+5 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 37
dsolve(4*x^2*(1+2*x)*diff(y(x),x$2)-2*x*(4-x)*diff(y(x),x)-(7+5*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} \left (5 x^{3}-10 x^{2}-40 x -16\right )}{\left (2 x +1\right )^{\frac {5}{4}} \sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 43
DSolve[4*x^2*(1+2*x)*y''[x]-2*x*(4-x)*y'[x]-(7+5*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\frac {2 c_2 (5 (x-4) x (x+2)-16)}{(2 x+1)^{5/4}}+35 c_1}{35 \sqrt {x}} \\ \end{align*}