Answer:
Hence the domain of the function y = 5 tan 5x is ,
and largest interval of definition for the solution is

Explanation:
Considering the differential equation

and the function y = 5 tan 5x
Find the domain of the function y = 5 tan 5x
Since
then determine the zeros of the denominator, cos 5x
The zeros of the denominator of cos 5x is

Hence the function y = 5 tan 5x exist on

Therefore, the domain of the function y = 5 tan 5x is

Differential the function y = 5 tan 5x with respect to x

Use trigonometry identity ,

Substitute


Therefore the function y = 5 tan 5x satisfies the differential equation

Now , Find the largest interval of the solution
Since the tangent function is periodic with period π so take interval

since , the function y = 5 tan 5x is not differentiatable at

Hence the domain of the function y = 5 tan 5x is ,
and largest interval of definition for the solution is
