The differential equation of family of curves whose tangents form an angle of `pi/4` with the hyperbola `xy=k` is (A) `dy/dx=(x^2+ky)/(x^2-ky)` (B) `dy/dx=(x+k)/(x-k)` (C) `dy/dx=-k/x^2` (D) `dy/dx=(x^2-k)/(x^2+k)`

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

The differential equation of the family of curves whose equation is (x-h)^2+(y-k)^2=a^2 , where a is a constant, is (A) [1+(dy/dx)^2]^3=a^2 (d^2y)/dx^2 (B) [1+(dy/dx)^2]^3=a^2 ((d^2y)/dx^2)^2 (C) [1+(dy/dx)]^3=a^2 ((d^2y)/dx^2)^2 (D) none of these

solve the differential equation (1+x^2)dy/dx=x

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

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

Solve: x+y dy/dx=(a^2((x dy/dx-y))/(x^2+y^2))

The differential equation of the family of curves y=k_(1)x^(2)+k_(2) is given by (where, k_(1) and k_(2) are arbitrary constants and y_(1)=(dy)/(dx), y_(2)=(d^(2)y)/(dx^(2)) )

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

Solve the differential equation : (dy)/(dx)-y/x=2x^2

Solve the differential equation: (dy)/(dx) = x^(2) (x-2)