Internal problem ID [8003]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 527.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (3 x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(3*x^2*diff(y(x),x$2)+x*(1+x)*diff(y(x),x)-(1+3*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \left (x^{2}+20 x +70\right )+c_{2} x \left (x^{2}+20 x +70\right ) \left (\int \frac {{\mathrm e}^{-\frac {x}{3}}}{x^{\frac {7}{3}} \left (x^{2}+20 x +70\right )^{2}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 78
DSolve[3*x^2*y''[x]+x*(1+x)*y'[x]-(1+3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x \left (x^2+20 x+70\right )-\frac {c_2 x \left (x^2+20 x+70\right ) \Gamma \left (\frac {2}{3},\frac {x}{3}\right )}{1680 \sqrt [3]{3}}+\frac {c_2 e^{-x/3} \left (x^3+19 x^2+54 x-18\right )}{1680 \sqrt [3]{x}} \]