Internal problem ID [8063]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 587.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (3-5 x \right ) y^{\prime }+\left (4-5 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 89
dsolve(x^2*(1-x)*diff(y(x),x$2)-x*(3-5*x)*diff(y(x),x)+(4-5*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2} \left (x^{3}-3 x^{2}+3 x -1\right )+c_{2} x^{2} \left (x^{3} \ln \left (x \right )-\ln \left (x -1\right ) x^{3}-3 x^{2} \ln \left (x \right )+3 \ln \left (x -1\right ) x^{2}+3 x \ln \left (x \right )-3 \ln \left (x -1\right ) x -x^{2}-\ln \left (x \right )+\ln \left (x -1\right )+\frac {5 x}{2}-\frac {11}{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 76
DSolve[x^2*(1-x)*y''[x]-x*(3-5*x)*y'[x]+(4-5*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{6} x^2 \left (6 c_1 x^3-18 c_1 x^2-6 c_2 x^2+18 c_1 x+15 c_2 x-6 c_2 (x-1)^3 \log (x-1)+6 c_2 (x-1)^3 \log (x)-6 c_1-11 c_2\right ) \]