Solve the initial value problem where y′′+4y′−21 y=0, y(1)=1, y′(1)=0 . Use t as the independent variable.

Step-by-step explanation:

y′′ + 4y′ − 21y = 0

The auxiliary equation is given by

m² + 4m - 21 = 0

We solve this using the quadratic formula. So

So, the solution of the equation is

where m₁ = 3 and m₂ = -7.

So,

Also,

Since y(1) = 1 and y'(1) = 0, we substitute them into the equations above. So,

Substituting A into (1) above, we have

Substituting B into A, we have

Substituting A and B into y, we have

So the solution to the differential equation is

b

step-by-step explanation: