ODE No. 897

$$y^{\prime }(x)=\frac{\sqrt{x}(-108x^{3/2}y(x)+18x^{9/2}-108x^{3/2}+x^9-18x^{6}y(x)+108x^{3}y(x{)}^2-216y(x{)}^3)}{36x^3-216y(x)-216}$$ ✓ Mathematica : cpu = 0.214607 (sec), leaf count = 79

DSolve[Derivative[1][y][x] == (Sqrt[x]*(-108*x^(3/2) + 18*x^(9/2) + x^9 - 108*x^(3/2)*y[x] - 18*x^6*y[x] + 108*x^3*y[x]^2 - 216*y[x]^3))/(-216 + 36*x^3 - 216*y[x]),y[x],x]
 

$$\{\{y(x)\to \frac{1}{6}(x^3-6)-\frac{1}{216(-\frac{1}{216}-\frac{1}{\sqrt{-62208x^{3/2}+c_1}})}\},\{y(x)\to \frac{1}{6}(x^3-6)-\frac{1}{216(-\frac{1}{216}+\frac{1}{\sqrt{-62208x^{3/2}+c_1}})}\}\}$$ ✓ Maple : cpu = 0.081 (sec), leaf count = 87

dsolve(diff(y(x),x) = (-108*x^(3/2)*y(x)+18*x^(9/2)-108*x^(3/2)-216*y(x)^3+108*x^3*y(x)^2-18*y(x)*x^6+x^9)*x^(1/2)/(-216*y(x)+36*x^3-216),y(x))
 

$$y\left(x\right)=\frac{\sqrt{9c_1-12x^{\frac{3}{2}}}{x}^3-3x^3+18}{6\sqrt{9c_1-12x^{\frac{3}{2}}}-18}$$