Internal problem ID [7319]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 600.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} \left (x +2\right ) y^{\prime \prime }-x \left (4-7 x \right ) y^{\prime }-\left (5-3 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 62
dsolve(2*x^2*(2+x)*diff(y(x),x$2)-x*(4-7*x)*diff(y(x),x)-(5-3*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{\frac {5}{2}}}{\left (x +2\right )^{\frac {7}{2}}}+\frac {c_{2} \left (\frac {\sqrt {2}\, \sqrt {x +2}\, \left (33 x^{2}+52 x +32\right )}{3}+5 \,\operatorname {arctanh}\left (\frac {\sqrt {2}\, \sqrt {x +2}}{2}\right ) x^{3}\right )}{\left (x +2\right )^{\frac {7}{2}} \sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 92
DSolve[2*x^2*(2+x)*y''[x]-x*(4-7*x)*y'[x]-(5-3*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {15 \sqrt {2} c_2 x^3 \text {arctanh}\left (\frac {\sqrt {x+2}}{\sqrt {2}}\right )-48 c_1 x^3+66 c_2 \sqrt {x+2} x^2+104 c_2 \sqrt {x+2} x+64 c_2 \sqrt {x+2}}{48 \sqrt {x} (x+2)^{7/2}} \\ \end{align*}