Internal problem ID [8025]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 549.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {8 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+2 x \left (34 x^{2}+5\right ) y^{\prime }-\left (-30 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(8*x^2*(1+2*x^2)*diff(y(x),x$2)+2*x*(5+34*x^2)*diff(y(x),x)-(1-30*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {1}{4}}}{\sqrt {2 x^{2}+1}}+\frac {c_{2} x^{\frac {1}{4}} \left (\int \frac {1}{\sqrt {2 x^{2}+1}\, x^{\frac {7}{4}}}d x \right )}{\sqrt {2 x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 54
DSolve[8*x^2*(1+2*x^2)*y''[x]+2*x*(5+34*x^2)*y'[x]-(1-30*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {3 c_1 x^{3/4}-4 c_2 \operatorname {Hypergeometric2F1}\left (-\frac {3}{8},\frac {1}{2},\frac {5}{8},-2 x^2\right )}{3 \sqrt {x} \sqrt {2 x^2+1}} \]