Question

Find the particular solution that satisfies the initial condition.

Differential equation                                         Initial condition

Answer 1

Step 1:

The differential equation is and the initial condition is .

Consider .

Re-write the equation.

Multiply and divide each side by 2.

Integrate on each side.

Step 2:

The solution of the differential equation is .

The initial condition is .

Substitute and in the solution of the differential equation.

Substitute in the solution of the differential equation.

Take exponents of each side.

Properties of natural logarithms: .

The solution of the differential equation is .

Solution:

The solution of the differential equation is .