The number of solutions of d y d x = y+1 x-1 , when y(1)=2 is

Step-by-step solution

The given differential equation is a first-order linear separable differential equation: dy dx = y+1 x-1 . Separating the variables, we have dy y+1 = dx x-1 . Integrating both sides, we get |y+1| = |x-1| + C , which can be written as y+1 = k(x-1) where k is a constant. The initial condition is given as y(1) = 2 . Substituting x=1 and y=2 into the equation y+1 = k(x-1) , we get 2+1 = k(1-1) , which simplifies to 3 = k(0) . Since 3 = 0 is a contradiction, there is no value of k that satisfies the initial condition y(