2.1551   ODE No. 1551

\[ -2 \left (\nu ^2 x^2+6\right ) y''(x)+\nu ^2 \left (\nu ^2 x^2+4\right ) y(x)+x^2 y^{(4)}(x)=0 \]

✓ Mathematica : cpu = 0.324606 (sec), leaf count = 110

DSolve[nu^2*(4 + nu^2*x^2)*y[x] - 2*(6 + nu^2*x^2)*Derivative[2][y][x] + x^2*Derivative[4][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {c_3 (1-x) e^{-\nu x} \left (\nu ^2 x^2+\nu ^2 x+\nu ^2+6 \nu x+6 \nu +15\right )}{x}+\frac {c_4 (1-x) e^{\nu x} \left (\nu ^2 x^2+\nu ^2 x+\nu ^2-6 \nu x-6 \nu +15\right )}{x}+\frac {c_1 e^{-\nu x}}{x}+\frac {c_2 e^{\nu x}}{x}\right \}\right \}\]

✓ Maple : cpu = 0.247 (sec), leaf count = 62

dsolve(x^2*diff(diff(diff(diff(y(x),x),x),x),x)-2*(nu^2*x^2+6)*diff(diff(y(x),x),x)+nu^2*(nu^2*x^2+4)*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {\left (c_{4} \nu ^{2} x^{3}+6 c_{4} \nu \,x^{2}+15 c_{4} x +c_{2} \right ) {\mathrm e}^{-\nu x}+{\mathrm e}^{\nu x} \left (c_{3} \nu ^{2} x^{3}-6 c_{3} \nu \,x^{2}+15 c_{3} x +c_{1} \right )}{x}\]