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

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

(x + y )(dy)/(dx) = 1

(x (dy) / (dx) -y) tan ^ (- 1) ((y) / (x)) = x

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 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. 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

Find the general solutions of the following differential equations. (i) (dy)/(dx) = e^(x+y) (ii) (dy)/(dx) = e^(y-x) (iii) (dy)/(dx) = (xy+y)/(yx+x) (iv) y(1+x)dx+x(1+y)dy = 0

(dy)/(dx) of (x^(y))(y^(x))=1

Solve the following differential equations: (dy)/(dx)=1+x+y+x y (ii) y-x(dy)/(dx)=a(y^2+(dy)/(dx))