Show that the differential equation representing one parameter family of curves `(x^2-y^2)=c(x^2+y^2)^2i s\ (x^3-3x y^2)dx=(y^3-3x^2y)dy`

(x^3+3x y^2)dx+(y^3+3x^2y)dy=0

Solve the differential equation: (dy)/(dx)+2y=sin\ 3x

Solve the differential equation (y+3x^2)(dx)/(dy)=x .

Solve the differential equation: (x+3y^2)(dy)/(dx)=y

Show that the differential equation of which y=2(x^2-1)+c e^-x^2 is a solution, is (dy)/(dx)+2x y=4x^3dot

Show that the differential equation y^3dy+(x+y^2)dx=0 can be reduced to a homogeneous equation.

Show that the differential equation of which y=2(x^2-1)+c e^-(x^2) is a solution, is (dy)/(dx)+2x y=4x^3dot

(2x^2+3y^2-7)x dx-(3x^2+2y^2-8)y dy=0

x^2y - x^3 dy/dx = y^2 cosx

STATEMENT-1 : y = e^(x) is a particular solution of (dy)/(dx) = y . STATEMENT-2 : The differential equation representing family of curve y = a cos omega t + b sin omega t , where a and b are parameters, is (d^(2)y)/(dt^(2)) - omega^(2) y = 0 . STATEMENT-3 : y = (1)/(2)x^(3)+c_(1)x+c_(2) is a general solution of (d^(2)y)/(dx^(2)) = 3x .