[" 7."(dx)/(dx)=e^(-ex)+x^(2)],[" (ii) "y-x(dy)/(dx)=3(1+x^(2)dx)]

(y-x(dy)/(dx))=3(1-x^(2)(dy)/(dx))

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

(dy)/(dx) + 3y = e^(-2x)

(dy)/(dx) + 3y = e^(-2x)

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

Express the following differential equations in the form f(x)dx+g(y)dy = 0 (i) (dy)/(dx) = (2y)/(x) (ii) x+y(dy)/(dx) = 0 (iii) (dy)/(dx) = e^(x-y) + x^(2).e^(-y) (iv) (dy)/(dx) + x^(2) = x^(2)e^(3y)

(dy)/(dx) = e^(2x-y) + x^(3) e^(-y)

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

Solve: (dy)/(dx)=e^(x+y) (ii) log((dy)/(dx))=a x+b y