Internal problem ID [6830]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 98.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (4 x +3\right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (4 x +3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 41
dsolve(x^2*(3+4*x)*diff(y(x),x$2)+x*(11+4*x)*diff(y(x),x)-(3+4*x)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \left (48 x^{2}+32 x +7\right )}{x^{3}}+c_{2} \hypergeom \left (\left [3, 5\right ], \left [\frac {13}{3}\right ], -\frac {4 x}{3}\right ) x^{\frac {1}{3}} \left (4 x +3\right )^{\frac {11}{3}} \]
✓ Solution by Mathematica
Time used: 0.872 (sec). Leaf size: 171
DSolve[x^2*(3+4*x)*y''[x]+x*(11+4*x)*y'[x]-(3+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-6 \sqrt [3]{2} c_2 (16 x (3 x+2)+7) \left (\log \left (4 x^{2/3}+2 \sqrt [3]{2} \sqrt [3]{4 x+3} \sqrt [3]{x}+(8 x+6)^{2/3}\right )-2 \log \left (\sqrt [3]{8 x+6}-2 \sqrt [3]{x}\right )+2 \sqrt {3} \cot ^{-1}\left (\frac {\sqrt [3]{x}+\sqrt [3]{8 x+6}}{\sqrt {3} \sqrt [3]{x}}\right )\right )+c_1 (16 x (3 x+2)+7)+24 c_2 \sqrt [3]{x} (4 x+3)^{2/3} (x (8 x (2 x+3)+25)+7)}{48 x^3} \\ \end{align*}