Internal problem ID [8016]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 540.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (x^{2}+2\right ) y^{\prime \prime }-x \left (-7 x^{2}+12\right ) y^{\prime }+\left (3 x^{2}+7\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(2*x^2*(2+x^2)*diff(y(x),x$2)-x*(12-7*x^2)*diff(y(x),x)+(7+3*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {7}{2}}}{\left (x^{2}+2\right )^{\frac {9}{4}}}+\frac {c_{2} x^{\frac {7}{2}} \left (\int \frac {\left (x^{2}+2\right )^{\frac {5}{4}}}{x^{4}}d x \right )}{\left (x^{2}+2\right )^{\frac {9}{4}}} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 57
DSolve[2*x^2*(2+x^2)*y''[x]-x*(12-7*x^2)*y'[x]+(7+3*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {x} \left (3 c_1 x^3-2 \sqrt [4]{2} c_2 \operatorname {Hypergeometric2F1}\left (-\frac {3}{2},-\frac {5}{4},-\frac {1}{2},-\frac {x^2}{2}\right )\right )}{3 \left (x^2+2\right )^{9/4}} \]