Find the particular solution of the differential equation that satisfies the boundary condition .

Question

Find the particular solution of the differential equation  that satisfies the boundary condition  .

Quizplus · Accepted Answer

The differential equation is separable, so we can write:
dy/dx = y(1 - y)
Separating variables and integrating, we get:
∫(1/y-1) dy = ∫dx + C
ln|y-1| = x + C
|y-1| = e^(x+C) = Ce^x
y - 1 = ±Ce^x
y = 1 ± Ce^x
Using the boundary condition y(0) = 2, we get:
2 = 1 ± C
C = 1 or C = -1
Therefore, the particular solution that satisfies the boundary condition is:
y = 1 + e^x  (since C = 1)

Find the Particular Solution of the Differential Equation That