Find the general solution for the differential equation.

Question

dx/dt=(2-x)sqrt(1-x)?

Answer 1

Step 1:

The differential equation is .

Solve the differential equation by variable separable method.

.

Apply integration on each side.

Let .

Differentiate with respect to on each side.

 

Substitute , and in the integral.

Step 2:

Assume .

.

Differentiate with respect to on each side.

Substitute , and in the integral.

Integral formula: .

Replace with .

.

Replace with .

.

General solution of the differential equation is .

Solution:

General solution of the differential equation is .