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),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 differential equation ((x+2y^3)dy)/(dx)=y is

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The general solution of the differential equation (dy)/(dx)=x^2/y^2 is

Solution of the differential equation (dy)/(dx)+(2y)/(x)=0 , where y(1)=1 , is

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Find the general solution of the differential equation (dy)/(dx)=(x+1)/(2-y),(y!=2)

Find the general solution of the differential equation (dy)/(dx)=(x+1)/(2-y),(y!=2)