Internal problem ID [7975]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 499.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{3}+1\right ) y^{\prime \prime }+7 x^{2} y^{\prime }+9 y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve((1+x^3)*diff(y(x),x$2)+7*x^2*diff(y(x),x)+9*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x}{\left (x^{3}+1\right )^{\frac {4}{3}}}+\frac {c_{2} x \left (\int \frac {{\left (\left (x +1\right ) \left (x^{2}-x +1\right )\right )}^{\frac {1}{3}}}{x^{2}}d x \right )}{\left (x^{3}+1\right )^{\frac {4}{3}}} \]
✓ Solution by Mathematica
Time used: 0.798 (sec). Leaf size: 118
DSolve[(1+x^3)*y''[x]+7*x^2*y'[x]+9*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-2 \sqrt {3} c_2 x \arctan \left (\frac {\sqrt {3} x}{2 \sqrt [3]{x^3+1}+x}\right )-6 c_2 \sqrt [3]{x^3+1}-2 c_2 x \log \left (\sqrt [3]{x^3+1}-x\right )+c_2 x \log \left (\sqrt [3]{x^3+1} x+\left (x^3+1\right )^{2/3}+x^2\right )+6 c_1 x}{6 \left (x^3+1\right )^{4/3}} \]