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

dy/dx का मान ज्ञात कीजिए यदि x=2at,y=at^2

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

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

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

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

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

If x^(3) dy + xy dx = x^(2) dy + 2y dx , y (2) = e and x gt 1 , then y(4) is equal to .

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

The family of curves represented by (dy)/(dx)=(x^(2)+x+1)/(y^(2)+y+1) and the family represented by (dy)/(dx)+(y^(2)+y+1)/(x^(2)+x+1)=0