Internal problem ID [7786]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 299.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {2 x y^{\prime \prime }-y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve(2*x*diff(y(x),x$2)-diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{2 i \sqrt {x}} \sqrt {\frac {\left (1+4 x \right ) \left (2 i \sqrt {x}-1\right )}{1+2 i \sqrt {x}}}+c_{2} {\mathrm e}^{-2 i \sqrt {x}} \sqrt {\frac {\left (1+4 x \right ) \left (1+2 i \sqrt {x}\right )}{2 i \sqrt {x}-1}} \]
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 59
DSolve[2*x*y''[x]-y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{2 i \sqrt {x}} \left (2 \sqrt {x}+i\right )+\frac {1}{8} c_2 e^{-2 i \sqrt {x}} \left (1+2 i \sqrt {x}\right ) \]