Internal problem ID [6805]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 74.
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: 0.062 (sec). Leaf size: 31
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)
\[ y \left (x \right ) = \frac {c_{1} \left (x +2\right )}{\left (1+\frac {2 x}{3}\right )^{\frac {2}{3}} x^{\frac {7}{3}}}+c_{2} \operatorname {hypergeom}\left (\left [2, 2\right ], \left [\frac {10}{3}\right ], -\frac {2 x}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.439 (sec). Leaf size: 167
DSolve[(3*x+2*x^2)*y''[x]+10*(1+x)*y'[x]+8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2^{2/3} c_2 (x+2) \left (\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 \log \left (2^{2/3} \sqrt [3]{2 x+3}-2 \sqrt [3]{x}\right )+2 \sqrt {3} \cot ^{-1}\left (\frac {\frac {2^{2/3} \sqrt [3]{2 x+3}}{\sqrt [3]{x}}+1}{\sqrt {3}}\right )\right )+4 c_1 (x+2)-8 c_2 \sqrt [3]{x} (2 x+3)^{2/3}}{4 x^{7/3} (2 x+3)^{2/3}} \\ \end{align*}