2(i)(x-y)(dy)/(dx)=x+2y

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

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

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

For each of the following differential equations verify that the accompanying functions a solution. (i) x(dy)/(dx)=y => y=a x (ii) x+y(dy)/(dx)=0 => y=+-sqrt(a^2-x^2) (iii) x(dy)/(dx)y+y^2 => y=a/(x+a) (iv) x^3(d^2y)/(dx^2)=1 => y=a x+b+1/(2x) (v) y=((dy)/(dx))^2 => y=1/4(x+-a)^2

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)

Solve (x+y(dy)/(dx))/(y-x(dy)/(dx))=x^2+2y^2+(y^4)/(x^2)