Internal problem ID [7400]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 681.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x -\frac {3}{4}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.112 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)+2*x^2*diff(y(x),x)+(x-3/4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {x}}+\frac {c_{2} {\mathrm e}^{-2 x} \left (2 x +1\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 33
DSolve[x^2*y''[x]+2*x^2*y'[x]+(x-3/4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 c_1-c_2 e^{-2 x} (2 x+1)}{4 \sqrt {x}} \\ \end{align*}