Please solve the following problem,

Verify that y = C*e ^4x + e ^3x, where c is a constant, is a solution to the differential equation y ' - 4y = -e ^3x .

Hi Swati please follow the following:

y ' is given by

y ' = 4C*e ^4x + 3e ^3x

We now substitute y ' and y into the left side of the equation and simplify

y ' - 4y = 4C*e ^4x + 3e ^3x - 4 (C*e ^4x + e ^3x)

= 4C*e ^4x + 3e ^3x - 4C*e ^4x - 4e ^3x

= 4C*e ^4x - 4C*e ^4x + e ^3x (3 - 4)

= - e ^3x

^enjoy...