" 5."x^(2)(dy)/(dx)+y=1

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

Solve y((dy)/(dx))^(2)+2x(dy)/(dx)-y=0 given that y(0)=sqrt(5)

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

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

Solution of differential equation y-x(dy)/(dx)=y^(2)+(dy)/(dx), when x=1,y=2, is

Find the general solution of the following D.E's (i) (dy)/(dx) = (x-y+3)/(2x-2y+5) (ii) (x-y)dy = (x+y+1) dx

If 2x=y^((1)/(5))+y^(-(1)/(5)) then (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=ky, then find the value of k .

For each of the following differential equations verify that the accompanying functions a solution. Differential Function (a) x(dy)/(dx)=y, y=a x (b) x+y(dy)/(dx)=0, y=+-sqrt(a^2-x^2) (c) x(dy)/(dx)y=y^2, y=a/(x+a) (d) x^3(d^2y)/(dx^2)=1, y=a x+b+1/(2x) (e) y=((dy)/(dx))^2, y=1/4(x+-a)^2

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