Internal problem ID [8050]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 574.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (1-x \right ) y^{\prime \prime }+x \left (7+x \right ) y^{\prime }+\left (9-x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 75
dsolve(x^2*(1-x)*diff(y(x),x$2)+x*(7+x)*diff(y(x),x)+(9-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (x^{4}+16 x^{3}+36 x^{2}+16 x +1\right )}{x^{3}}+\frac {c_{2} \left (x^{4} \ln \left (x \right )+16 x^{3} \ln \left (x \right )+36 x^{2} \ln \left (x \right )+40 x^{3}+16 x \ln \left (x \right )+150 x^{2}+\ln \left (x \right )+\frac {280 x}{3}+\frac {25}{3}\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 78
DSolve[x^2*(1-x)*y''[x]+x*(7+x)*y'[x]+(9-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {5 c_2 \left (24 x^3+90 x^2+56 x+5\right )+3 c_1 \left (x^4+16 x^3+36 x^2+16 x+1\right )+3 c_2 \left (x^4+16 x^3+36 x^2+16 x+1\right ) \log (x)}{3 x^3} \]