Internal problem ID [7810]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 325.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(x^2*diff(y(x),x$2)+(5/3*x+x^2)*diff(y(x),x)-1/3*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (3 x -1\right )}{x}+\frac {c_{2} \left (3 x -1\right ) \left (\int \frac {x^{\frac {1}{3}} {\mathrm e}^{-x}}{\left (3 x -1\right )^{2}}d x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 47
DSolve[x^2*y''[x]+(5/3*x+x^2)*y'[x]-1/3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {-3 c_1 x+3 c_2 e^{-x} \sqrt [3]{x}+c_2 (1-3 x) \Gamma \left (\frac {1}{3},x\right )+c_1}{3 x} \]