Internal problem ID [7984]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 508.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}+3 x \right ) y^{\prime \prime }+10 \left (1+x \right ) y^{\prime }+8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 53
dsolve((3*x+2*x^2)*diff(y(x),x$2)+10*(1+x)*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x +2\right )}{x^{\frac {7}{3}} \left (2 x +3\right )^{\frac {2}{3}}}+\frac {c_{2} \left (x +2\right ) \left (\int \frac {x^{\frac {4}{3}}}{\left (x +2\right )^{2} \left (2 x +3\right )^{\frac {1}{3}}}d x \right )}{x^{\frac {7}{3}} \left (2 x +3\right )^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 0.28 (sec). Leaf size: 245
DSolve[(3*x+2*x^2)*y''[x]+10*(1+x)*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2\ 2^{2/3} \sqrt {3} c_2 (x+2) \arctan \left (\frac {\sqrt {3} \sqrt [3]{x}}{\sqrt [3]{x}+2^{2/3} \sqrt [3]{2 x+3}}\right )+2^{2/3} c_2 x \log \left (2 x^{2/3}+2^{2/3} \sqrt [3]{2 x+3} \sqrt [3]{x}+\sqrt [3]{2} (2 x+3)^{2/3}\right )+2\ 2^{2/3} c_2 \log \left (2 x^{2/3}+2^{2/3} \sqrt [3]{2 x+3} \sqrt [3]{x}+\sqrt [3]{2} (2 x+3)^{2/3}\right )+4 c_1 x-8 c_2 \sqrt [3]{x} (2 x+3)^{2/3}-2\ 2^{2/3} c_2 (x+2) \log \left (2^{2/3} \sqrt [3]{2 x+3}-2 \sqrt [3]{x}\right )+8 c_1}{4 x^{7/3} (2 x+3)^{2/3}} \]