2.1775   ODE No. 1775

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

✓ Mathematica : cpu = 0.159932 (sec), leaf count = 29

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

\[\left \{\left \{y(x)\to c_2 e^{a \log (x+1)+\frac {-a-c_1}{x}}\right \}\right \}\]

✓ Maple : cpu = 0.244 (sec), leaf count = 31

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

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