Internal problem ID [7193]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 472.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(3-16*x^2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sqrt {x}\, \sinh \left (2 x \right )+c_{2} \sqrt {x}\, \cosh \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 32
DSolve[4*x^2*y''[x]-4*x*y'[x]+(3-16*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-2 x} \sqrt {x} \left (c_2 e^{4 x}+4 c_1\right ) \\ \end{align*}