Internal problem ID [6915]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 183.
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 (4 x +1\right ) y^{\prime }-\left (49+27 x \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 30
dsolve(4*x^2*(1+x)*diff(y(x),x$2)+4*x*(1+4*x)*diff(y(x),x)-(49+27*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} x^{\frac {7}{2}}}{\left (x +1\right )^{2}}+\frac {c_{2} \left (7 x +6\right )}{\left (x +1\right )^{2} x^{\frac {7}{2}}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 36
DSolve[4*x^2*(1+x)*y''[x]+4*x*(1+4*x)*y'[x]-(49+27*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {42 c_1 x^7-c_2 (7 x+6)}{42 x^{7/2} (x+1)^2} \\ \end{align*}