2.454   ODE No. 454

\[ a x^2 y'(x)^2-(a-1) a x^2-2 a x y(x) y'(x)+y(x)^2=0 \]

✓ Mathematica : cpu = 0.197509 (sec), leaf count = 235

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

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

✓ Maple : cpu = 0.139 (sec), leaf count = 106

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

\[y \left (x \right ) = \sqrt {-a}\, x\]