Internal problem ID [8071]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 595.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {16 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x \left (9 x^{2}+1\right ) y^{\prime }+\left (49 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve(16*x^2*(1+x^2)*diff(y(x),x$2)+8*x*(1+9*x^2)*diff(y(x),x)+(1+49*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {1}{4}}}{x^{2}+1}+\frac {c_{2} x^{\frac {1}{4}} \ln \left (x \right )}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 26
DSolve[16*x^2*(1+x^2)*y''[x]+8*x*(1+9*x^2)*y'[x]+(1+49*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x} (c_2 \log (x)+c_1)}{x^2+1} \]