`x(x^2-1)(dy)/(dx)=1; y=0w h e nx=2`

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

x(2y-1)dx+(x^(2)+1)dy=0

For each of the following initial value problems verify that the accompanying functions is a solution. (i) x(dy)/(dx)=1, y(1)=0 => y=logx (ii) (dy)/(dx)=y , y(0)=1 => y=e^x (iii) (d^2y)/(dx^2)+y=0, y(0)=0, y^(prime)(0)=1 => y=sinx (iv) (d^2y)/(dx^2)-(dy)/(dx)=0, y(0)=2, y^(prime)(0)=1 => y=e^x+1 (v) (dy)/(dx)+y=2, y(0)=3 => y=e^(-x)+2

(x+1)(dy)/(dx) -1 = 2e^(-y) , y=0, " when " x=1

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

(1+e^(x))/(y)(dy)/(dx)=e^(x), when y=1, x=0

Find the derivative of f(x)={(x-1)/(2x^2-7x+5)w h e nx!=1=1/3w h e nx=1a tx=1.

Solve the differential equation: (i) (1+y^(2))+(x-e^( tan ^(-1)y))(dy)/(dx)=0 (ii) x(dy)/(dx)+cos^(2)y=tan y(dy)/(dx)

If y satisfies (dy)/(dx)=(e^(y))/(x^(2))-(1)/(x) and y(1)=0 then the value of e^(y(2)) is