Let `y_(1)` and `y_(2)` be two different solutions of the equation
`(dy)/(dx)+P(x).y=Q(x)`. Then `alphay_(1)+betay_(2)` will be solution of the given equation if `alpha + beta=……………….`

The solution of the equation (dy)/(dx)=cos(x-y) is

The solution of the equation (dy)/(dx)=(x+y)/(x-y) , is

The general solution of the equation (dy)/(dx)=1+x y is

The general solution of the equation, x((dy)/(dx)) = y ln (y/x) is

If y_1 and y_2 are two solutions to the differential equation (dy)/(dx)+P(x)y=Q(x) . Then prove that y=y_1+c(y_1-y_2) is the general solution to the equation where c is any constant.

If y_1 and y_2 are two solutions to the differential equation (dy)/(dx)+P(x)y=Q(x) . Then prove that y=y_1+c(y_1-y_2) is the general solution to the equation where c is any constant.

The solution of the equation (dy)/(dx) +1/xtany =(1)/(x^(2))tan y sin y is:

The solution of differential equation x(dy)/(dx)=y is :

If (y_(1),y_(2)) are two solutions of the differential (dy)/(dx)+p(x).y=Q(x) Then prove that y=y_(1)+C(y_(1)-y_(2)) is the genral solution of the equation where C is any constant. For what relation between the constant alpha,beta will the linear combination alphay_(1)+betay_(2) also be a Solution.

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by