Internal problem ID [8067]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 591.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+2 x \left (-x^{2}+4\right ) y^{\prime }+\left (7 x^{2}+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(4*x^2*diff(y(x),x$2)+2*x*(4-x^2)*diff(y(x),x)+(1+7*x^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{4}-16 x^{2}+32\right )}{\sqrt {x}}+\frac {c_{2} \left (x^{4}-16 x^{2}+32\right ) \left (\int \frac {{\mathrm e}^{\frac {x^{2}}{4}}}{x \left (x^{4}-16 x^{2}+32\right )^{2}}d x \right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 68
DSolve[4*x^2*y''[x]+2*x*(4-x^2)*y'[x]+(1+7*x^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \left (x^4-16 x^2+32\right ) \operatorname {ExpIntegralEi}\left (\frac {x^2}{4}\right )-4 c_2 e^{\frac {x^2}{4}} \left (x^2-12\right )+2048 c_1 \left (x^4-16 x^2+32\right )}{2048 \sqrt {x}} \]