Internal problem ID [8049]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 573.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (4 x +5\right ) y^{\prime }+\left (9+4 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve(x^2*(1-2*x)*diff(y(x),x$2)-x*(5+4*x)*diff(y(x),x)+(9+4*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x^{3} \left (8 x +1\right )}{\left (-1+2 x \right )^{6}}+\frac {c_{2} x^{3} \left (\frac {4 x^{4}}{3}-\frac {16 x^{3}}{3}-8 x \ln \left (x \right )+12 x^{2}-\ln \left (x \right )+\frac {203 x}{128}-\frac {3125}{1024}\right )}{\left (-1+2 x \right )^{6}} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 63
DSolve[x^2*(1-2*x)*y''[x]-x*(5+4*x)*y'[x]+(9+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^3 \left (c_2 \left (4096 x^4-16384 x^3+36864 x^2+4872 x-9375\right )-48 c_1 (8 x+1)-3072 c_2 (8 x+1) \log (x)\right )}{384 (1-2 x)^6} \]