Internal problem ID [7950]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 473.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 y^{\prime \prime } x^{2}-4 y^{\prime } x +\left (4 x^{2}+3\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2+3)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \sqrt {x}\, \sin \left (x \right )+c_{2} \sqrt {x}\, \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 39
DSolve[4*x^2*y''[x]-4*x*y'[x]+(4*x^2+3)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-i x} \sqrt {x} \left (2 c_1-i c_2 e^{2 i x}\right ) \]