Internal problem ID [7749]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 262.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve((4*x^3-14*x^2-2*x)*diff(y(x),x$2)-(6*x^2-7*x+1)*diff(y(x),x)+(6*x-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (x -1\right )+c_{2} \sqrt {x}\, \left (2 x +1\right ) \]
✓ Solution by Mathematica
Time used: 6.298 (sec). Leaf size: 26
DSolve[(4*x^3-14*x^2-2*x)*y''[x]-(6*x^2-7*x+1)*y'[x]+(6*x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 (x-1)-2 c_2 \sqrt {x} (2 x+1) \]