The function is
.
Apply derivative on each side with respect to
.

Use sum rule of derivative :
.

The product rule of derivative :
.
Consider
and
.
and
.

.
The differential equation is
.
Consider left hand side
.
Substitute
.

Simplify the expression.
\ 

Substitute
.

Therefore,
is a solution of differential equation
.
is a solution of differential equation
.