$\"\"$

\

The function is $\"\"$ .

\

Apply the first derivative each side.

\

$\"\"$

\

The derivative sum rule.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Apply the second derivative each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The differential equation is $\"\"$ .

\

Consider the L.H.S.

\

$\"\"$

\

$\"\"$

\

Substitute the values of $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The initial condition $\"\"$ when $\"\"$ yields.

\

Substitute $\"\"$ in the function $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The initial condition $\"\"$ when $\"\"$ and $\"\"$ yields.

\

Substitute $\"\"$ in the function $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute the values of $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

The particular solution is $\"\"$ .