Question
Asked Feb 19, 2020
1 views

Find y as a function of t if

5y′′+31y=0

y(0)=4,y′(0)=7
y(t)=

check_circle

Expert Answer

Solving the given differential equation

The given differential equation is 

5y''+31y=0   ......(1)

and the initial condition is y(0)=4 and y'(0)=7

To get the auxiliary equation we replace y by 1 and y'' by m2

So, the auxiliary equation is 

5m2+31=0

The roots of the above equation are

Advanced Math homework question answer, step 1, image 1

so, the solution of the differential equation is 

Advanced Math homework question answer, step 1, image 2......(1)

where A and B are arbitrary constants

 

Find the arbitrary constants

Using y(0)=4 we get

4=A*1+B*0

A=4

Differentiating (1) with respect to t we get

Advanced Math homework question answer, step 2, image 1

Now using y'(0)=7 we get

Advanced Math homework question answer, step 2, image 2

 

...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.