ODE No. 1512

\[ \left (1-a^2\right ) x y'(x)+x^3 y^{(3)}(x)+3 x^2 y''(x)=0 \]

✓ Mathematica : cpu = 0.0376309 (sec), leaf count = 29

DSolve[(1 - a^2)*x*Derivative[1][y][x] + 3*x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to -\frac {c_1 x^{-a}}{a}+\frac {c_2 x^a}{a}+c_3\right \}\right \}\]

✓ Maple : cpu = 0.012 (sec), leaf count = 18

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+(-a^2+1)*x*diff(y(x),x)=0,y(x))

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