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 $\"\"$ .