ODE No. 593

$$y^{\prime }(x)=\frac{e^{x}F(y(x{)}^{3/2}-\frac{3e^x}{2})}{\sqrt{y(x)}}$$ ✓ Mathematica : cpu = 0.408659 (sec), leaf count = 221

DSolve[Derivative[1][y][x] == (E^x*F[(-3*E^x)/2 + y[x]^(3/2)])/Sqrt[y[x]],y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}(\frac{\sqrt{K[2]}}{F(K[2{]}^{3/2}-\frac{3e^x}{2})-1}-{\int }_1^x(\frac{3e^{K[1]}F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})\sqrt{K[2]}{F}^{\prime }(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})}{2{(F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})-1)}^2}-\frac{3e^{K[1]}\sqrt{K[2]}{F}^{\prime }(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})}{2(F(K[2{]}^{3/2}-\frac{3e^{K[1]}}{2})-1)})dK[1])dK[2]+{\int }_1^x-\frac{e^{K[1]}F(y(x{)}^{3/2}-\frac{3e^{K[1]}}{2})}{F(y(x{)}^{3/2}-\frac{3e^{K[1]}}{2})-1}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.308 (sec), leaf count = 35

dsolve(diff(y(x),x) = F(y(x)^(3/2)-3/2*exp(x))/y(x)^(1/2)*exp(x),y(x))
 

$${\int }_{\mathit{\text{\_b}}}^{y\left(x\right)}\frac{\sqrt{\mathit{\text{\_a}}}}{F({\mathit{\text{\_a}}}^{\frac{3}{2}}-\frac{3{\mathrm{e}}^x}{2})-1}d\mathit{\text{\_a}}-{\mathrm{e}}^x-c_1=0$$