ODE No. 389

\[ y'(x)^2-(4 y(x)+1) y'(x)+y(x) (4 y(x)+1)=0 \] Mathematica : cpu = 0.0741217 (sec), leaf count = 57

DSolve[y[x]*(1 + 4*y[x]) - (1 + 4*y[x])*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {1}{4} e^{x-4 c_1} \left (-e^x+2 e^{2 c_1}\right )\right \},\left \{y(x)\to \frac {1}{4} e^{x+2 c_1} \left (-2+e^{x+2 c_1}\right )\right \}\right \}\] Maple : cpu = 0.75 (sec), leaf count = 71

dsolve(diff(y(x),x)^2-(4*y(x)+1)*diff(y(x),x)+(4*y(x)+1)*y(x) = 0,y(x))
 

\[y \left (x \right ) = -{\frac {1}{4}}\]