2.525   ODE No. 525

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

✓ Mathematica : cpu = 0.094588 (sec), leaf count = 129

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

\[\left \{\left \{y(x)\to c_1 \exp \left (\frac {1}{2} \left (\frac {a x^2}{2}+\frac {1}{2} \sqrt {a} x \sqrt {a x^2-8}-4 \tanh ^{-1}\left (\frac {\sqrt {a} x}{\sqrt {a x^2-8}}\right )\right )\right )\right \},\left \{y(x)\to c_1 \exp \left (\frac {1}{2} \left (\frac {a x^2}{2}-\frac {1}{2} \sqrt {a} x \sqrt {a x^2-8}+4 \tanh ^{-1}\left (\frac {\sqrt {a} x}{\sqrt {a x^2-8}}\right )\right )\right )\right \}\right \}\]

✓ Maple : cpu = 0.083 (sec), leaf count = 122

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

\[y \left (x \right ) = c_{1} \left (\frac {x \,a^{2}}{\sqrt {a^{2}}}+\sqrt {a^{2} x^{2}-8 a}\right )^{-\frac {2 a}{\sqrt {a^{2}}}} {\mathrm e}^{\frac {x \left (a x +\sqrt {a^{2} x^{2}-8 a}\right )}{4}}\]