Question

Find the particular solution that satisfies the initial condition.

Differential equation                                              Initial condition       

Answer 1

Step 1:

The differential equation is .

The initial condition is .

Multiply each side by 2.

Apply integral on each side.

Apply formula .

The solution of the differential equation is .

Step 2:

The initial condition is .

Substitute and in .

Substitute in the solution of the differential equation.

Take exponents of each side.

Apply natural logarithms formula .

The solution of the differential equation is .

Solution:

The solution of the differential equation is .