Internal problem ID [8061]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 585.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }+3 x y^{\prime }+\left (1+4 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(x^2*(1-2*x)*diff(y(x),x$2)+3*x*diff(y(x),x)+(1+4*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}-\frac {c_{2} \left (-8 x^{3}+18 x^{2}+3 \ln \left (x \right )-18 x \right )}{3 x} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 36
DSolve[x^2*(1-2*x)*y''[x]+3*x*y'[x]+(1+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2}{3} c_2 \left (4 x^2-9 x+9\right )+\frac {c_1}{x}+\frac {c_2 \log (x)}{x} \]