2.1509   ODE No. 1509

\[ \left (\left (1-4 \nu ^2\right ) x+4 x^3\right ) y'(x)+\left (4 \nu ^2-1\right ) y(x)+x^3 y^{(3)}(x)=0 \]

✓ Mathematica : cpu = 0.0099202 (sec), leaf count = 34

DSolve[(-1 + 4*nu^2)*y[x] + ((1 - 4*nu^2)*x + 4*x^3)*Derivative[1][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 x J_{\nu }(x){}^2+c_3 x Y_{\nu }(x){}^2+c_2 x J_{\nu }(x) Y_{\nu }(x)\right \}\right \}\]

✓ Maple : cpu = 0.064 (sec), leaf count = 29

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+(4*x^3+(-4*nu^2+1)*x)*diff(y(x),x)+(4*nu^2-1)*y(x)=0,y(x))
 

\[y \left (x \right ) = x \left (\operatorname {BesselY}\left (\nu , x\right )^{2} c_{2} +\operatorname {BesselY}\left (\nu , x\right ) \operatorname {BesselJ}\left (\nu , x\right ) c_{3} +\operatorname {BesselJ}\left (\nu , x\right )^{2} c_{1} \right )\]