The solution of a certain differential equation is of the form y(t)=aexp(7t)+bexp(11t), where a and b are constants. the solution has initial conditions y(0)=1 and y′(0)=4. find the solution by using the initial conditions to get linear equations for a and b.

Step-by-step explanation:

Given that the solution of a certain differential equation is of the form

Use the initial conditions

i) y(0) =1

... I

ii) y'(0) = 4

Find derivative of y first and then substitute

Now using I and II we solve for a and b

Substitute b = 1-a in II

Hence solution is

a

step-by-step explanation:

a