Solve `(dy)/(dx)+y phi'(x)=phi(x).phi'(x), "where" " "phi(x)` is a given function.

Solve (dy)/(dx)=(yphi'(x)-y^(2))/(phi(x)),"where" " "phi(x) is a given function.

Solve (dy)/(dx)+2y=cos x.

Solve y-x(dy)/(dx)=a(y^(2)+(dy)/(dx))

Solve 2(dy)/(dx)=(y)/(x)+(y^(2))/(x^(2))

Solve (dy)/(dx)=e^(x-y)+x^(2)e^(-y) .

Solve (x+y)^(2)(dy)/(dx)=a^(2)

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.

{phi} = phi

"Let "f(x)=phi(x)+Psi(x), phi'(x) and Psi'(x) are finite and definite. Then,