2.1799   ODE No. 1799

\[ y(x)^3 y''(x)-a=0 \]

✓ Mathematica : cpu = 1.53116 (sec), leaf count = 88

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {a+c_1{}^2 x^2+2 c_2 c_1{}^2 x+c_2{}^2 c_1{}^2}}{\sqrt {c_1}}\right \},\left \{y(x)\to \frac {\sqrt {a+c_1{}^2 x^2+2 c_2 c_1{}^2 x+c_2{}^2 c_1{}^2}}{\sqrt {c_1}}\right \}\right \}\]

✓ Maple : cpu = 0.297 (sec), leaf count = 46

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

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