Internal problem ID [7005]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 274.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(4*diff(y(x),x$2)+3*(2-x^2)/(1-x^2)^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \left (x^{2}-1\right )^{\frac {3}{4}}+c_{2} \left (x^{2}-1\right )^{\frac {1}{4}} x \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 51
DSolve[4*y''[x]+3*(2-x^2)/(1-x^2)^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x^2-1} \left (c_2 Q_{\frac {1}{2}}^{\frac {1}{2}}(x)+\frac {\sqrt {\frac {2}{\pi }} c_1 x}{\sqrt [4]{1-x^2}}\right ) \\ \end{align*}