Internal problem ID [6863]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 131.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 x^{2} y^{\prime \prime }+4 x \left (2 x^{2}+x +6\right ) y^{\prime }+\left (18 x^{2}+5 x +1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 1.297 (sec). Leaf size: 42
dsolve(16*x^2*diff(y(x),x$2)+4*x*(6+x+2*x^2)*diff(y(x),x)+(1+5*x+18*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} {\mathrm e}^{-\frac {\left (x +1\right ) x}{4}}}{x^{\frac {1}{4}}}+\frac {c_{2} {\mathrm e}^{-\frac {\left (x +1\right ) x}{4}} \left (\int \frac {{\mathrm e}^{\frac {\left (x +1\right ) x}{4}}}{x}d x \right )}{x^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 51
DSolve[16*x^2*y''[x]+4*x*(6+x+2*x^2)*y'[x]+(1+5*x+18*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-\frac {1}{4} x (x+1)} \left (c_2 \int _1^x\frac {e^{\frac {1}{4} K[1] (K[1]+1)}}{K[1]}dK[1]+c_1\right )}{\sqrt [4]{x}} \\ \end{align*}