2.475   ODE No. 475

\[ 4 y(x) y'(x)^2+2 x y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.068638 (sec), leaf count = 113

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

\[\left \{\left \{y(x)\to -\frac {1}{2} e^{2 c_1} \sqrt {-2 x+e^{4 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{2 c_1} \sqrt {-2 x+e^{4 c_1}}\right \},\left \{y(x)\to -\frac {1}{2} e^{2 c_1} \sqrt {2 x+e^{4 c_1}}\right \},\left \{y(x)\to \frac {1}{2} e^{2 c_1} \sqrt {2 x+e^{4 c_1}}\right \}\right \}\]

✓ Maple : cpu = 0.735 (sec), leaf count = 67

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

\[y \left (x \right ) = -\frac {i x}{2}\]