Internal problem ID [8020]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 544.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (8 x^{2}+3\right ) y^{\prime }-\left (-4 x^{2}+3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(2*x^2*(1+x^2)*diff(y(x),x$2)+x*(3+8*x^2)*diff(y(x),x)-(3-4*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{\left (x^{2}+1\right )^{\frac {1}{4}} x^{\frac {3}{2}}}+\frac {c_{2} \left (\int \frac {x^{\frac {3}{2}}}{\left (x^{2}+1\right )^{\frac {3}{4}}}d x \right )}{\left (x^{2}+1\right )^{\frac {1}{4}} x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 60
DSolve[2*x^2*(1+x^2)*y''[x]+x*(3+8*x^2)*y'[x]-(3-4*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {c_2 \operatorname {Hypergeometric2F1}\left (\frac {1}{4},\frac {3}{4},\frac {5}{4},-x^2\right )}{x \sqrt [4]{x^2+1}}+\frac {c_1}{x^{3/2} \sqrt [4]{x^2+1}}+\frac {c_2}{x} \]