Internal problem ID [6905]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 173.
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 +1\right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 42
dsolve(4*x^2*(1+x)*diff(y(x),x$2)+4*x*(3+8*x)*diff(y(x),x)-(5-49*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sqrt {x}}{\left (x +1\right )^{4}}+\frac {c_{2} \left (6 \ln \relax (x ) x^{3}-18 x^{2}-9 x -2\right )}{\left (x +1\right )^{4} x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 50
DSolve[4*x^2*(1+x)*y''[x]+4*x*(3+8*x)*y'[x]-(5-49*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6 c_1 x^3+6 c_2 x^3 \log (x)-c_2 (9 x (2 x+1)+2)}{6 x^{5/2} (x+1)^4} \\ \end{align*}