Solve the initial value problem

y′′+3y=0

y(0)=1
y′(0)=1

The solution is

Step-by-step explanation:

The question is:

Solve the initial value problem

y′′+3y'=0

y(0)=1

y′(0)=1

Step-by-step explanation:

First, we will write the characteristic equation, which is

Then, we will solve for

becomes

∴ or

or

Hence,

Since the two roots are distinct, that is,

The general solution is

Then,

Then, for

Now, from the question

y(0)=1

y′(0)=1

Then,

Then,

........ (1)

Also,

Then,

....... (2)

∴

From equation (1)

Then,

Hence, and

Then, the solution becomes

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step-by-step explanation: