2.465   ODE No. 465

\[ y(x) y'(x)^2+2 x y'(x)-9 y(x)=0 \]

✓ Mathematica : cpu = 0.0373762 (sec), leaf count = 107

DSolve[-9*y[x] + 2*x*Derivative[1][y][x] + y[x]*Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\text {Solve}\left [\int \frac {y(x)}{x \left (\frac {y(x)^2}{x^2}-\sqrt {\frac {9 y(x)^2}{x^2}+1}+1\right )}d\frac {y(x)}{x}=-\log (x)+c_1,y(x)\right ],\text {Solve}\left [\int \frac {y(x)}{x \left (\frac {y(x)^2}{x^2}+\sqrt {\frac {9 y(x)^2}{x^2}+1}+1\right )}d\frac {y(x)}{x}=-\log (x)+c_1,y(x)\right ]\right \}\]

✓ Maple : cpu = 0.1 (sec), leaf count = 210

dsolve(y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-9*y(x) = 0,y(x))
 

\[\frac {c_{1} x \left (x +\sqrt {x^{2}+9 y \left (x \right )^{2}}\right ) {\left (\frac {-x -\sqrt {x^{2}+9 y \left (x \right )^{2}}}{y \left (x \right )}\right )}^{{2}/{7}}}{\left (x \sqrt {x^{2}+9 y \left (x \right )^{2}}+x^{2}+y \left (x \right )^{2}\right ) {\left (\frac {x \sqrt {x^{2}+9 y \left (x \right )^{2}}+x^{2}+y \left (x \right )^{2}}{y \left (x \right )^{2}}\right )}^{{1}/{7}}}+x = 0\]