" (i) "x(x^(2)-1)(dy)/(dx)=1,y=0" when "x=2" A "cos((dy)/(d))

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

The solution of the equation x^(2)(d^(2)y)/(dx^(2))=log x when x=1,y=0 and (dy)/(dx)=-1 is

cos((dy)/(dx))=a(a in R);y=1 when x=0

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

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

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)

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

Find (dy)/(dx) , when: y=x^((cos^(-1)x))

(d^(2)y)/(dx^(2))=(1)/(1+x^(2)) whenx =0,y=0 and (dy)/(dx)=0

Find dy/dx when: y= cos^-1((1-x^2)/(1+x^2))