2.463   ODE No. 463

\[ y(x) y'(x)^2-e^{2 x}=0 \]

✓ Mathematica : cpu = 0.0435761 (sec), leaf count = 47

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

\[\left \{\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (-e^x+c_1\right ){}^{2/3}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \left (e^x+c_1\right ){}^{2/3}\right \}\right \}\]

✓ Maple : cpu = 0.098 (sec), leaf count = 50

dsolve(y(x)*diff(y(x),x)^2-exp(2*x) = 0,y(x))
 

\[-\frac {\sqrt {{\mathrm e}^{2 x} y \left (x \right )}}{\sqrt {y \left (x \right )}}+\frac {2 y \left (x \right )^{{3}/{2}}}{3}+c_{1} = 0\]