d^2y/dx^2−2dy/dx+10y=0 where x=0.y=0 and dy/dx=4?x=0.y=0 and dy/dx=4?

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-08-12

d2ydx22dydx+10y=0 where x=0.y=0 and dydx=4?x=0.y=0 and dydx=4?

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-08-13Added 109 answers

The given differential is d2ydx22dydx+10y=0 where x=0.y=0 and dydx=4.
The auxilary equation is given by m22m+10=0
m=2+(440)m=2±2(110)m=1±110m=1±9m=1±3i
Therefore the general olution is given by y(x)=ex(c1cos(3x)+c2sin(3x))
When x=0,y=0 therefore c1=0. Therefore y=c2ex(sin(3x))dyx=c2ex(sin(3x)+3cos(3x))
Again when x=0,dydx=4, this implies that 4=3e2
Therefore the solution is y=(4ex3)sin(3x)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?