2.1721   ODE No. 1721

1. Problem in Latex
2. Mathematica input
3. Maple input

$$-\frac{ay(x{)}^3{f}^{\prime }(x)}{a+2}+\frac{af(x{)}^{2}y(x{)}^4}{(a+2{)}^2}-\frac{(a-1)y^{\prime }(x{)}^2}{a}-f(x)y(x{)}^2{y}^{\prime }(x)+y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 21.3503 (sec), leaf count = 41

$$\left\{\{y(x)\to -\frac{(a+2)(x+c_1){}^a}{a{\int }_1^{x}f(K[3])(c_1+K[3]){}^{a}dK[3]+c_2}\}\right\}$$ ✗ Maple : cpu = 0. (sec), leaf count = 0 , could not solve

dsolve(diff(diff(y(x),x),x)*y(x)-(a-1)/a*diff(y(x),x)^2-f(x)*y(x)^2*diff(y(x),x)+a/(a+2)^2*f(x)^2*y(x)^4-a/(a+2)*diff(f(x),x)*y(x)^3=0,y(x))