#### 2.593   ODE No. 593

$y'(x)=\frac {e^x F\left (y(x)^{3/2}-\frac {3 e^x}{2}\right )}{\sqrt {y(x)}}$ Mathematica : cpu = 0.386065 (sec), leaf count = 221

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]}}{F\left (K[2]^{3/2}-\frac {3 e^x}{2}\right )-1}-\int _1^x\left (\frac {3 e^{K[1]} F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right ) \sqrt {K[2]} F'\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{2 \left (F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1\right )^2}-\frac {3 e^{K[1]} \sqrt {K[2]} F'\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{2 \left (F\left (K[2]^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1\right )}\right )dK[1]\right )dK[2]+\int _1^x-\frac {e^{K[1]} F\left (y(x)^{3/2}-\frac {3 e^{K[1]}}{2}\right )}{F\left (y(x)^{3/2}-\frac {3 e^{K[1]}}{2}\right )-1}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.391 (sec), leaf count = 35

$\left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\sqrt {{\it \_a}} \left ( F \left ( {{\it \_a}}^{{\frac {3}{2}}}-{\frac {3\,{{\rm e}^{x}}}{2}} \right ) -1 \right ) ^{-1}}\,{\rm d}{\it \_a}-{{\rm e}^{x}}-{\it \_C1}=0 \right \}$