ODE No. 1301

\[ \left (a x^2+b x\right ) y''(x)-2 a y(x)+2 b y'(x)=0 \]

✓ Mathematica : cpu = 0.0184684 (sec), leaf count = 31

DSolve[-2*a*y[x] + 2*b*Derivative[1][y][x] + (b*x + a*x^2)*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to \frac {c_2 (a x+b)^3}{3 a x}+\frac {c_1}{x}\right \}\right \}\]

✓ Maple : cpu = 0.026 (sec), leaf count = 19

dsolve((a*x^2+b*x)*diff(diff(y(x),x),x)+2*b*diff(y(x),x)-2*a*y(x)=0,y(x))

\[y \left (x \right ) = \frac {c_{1} +c_{2} \left (a x +b \right )^{3}}{x}\]