Thread: Third order DE-similiar to previous

1. Third order DE-similiar to previous

y = c1 + c2cos x + c3sin x is the general solution of the differential equation y''' + y' = 0 on (-infinity, infinity). Find a member of the family that is a solution with initial conditions y(pi) = 0, y'(pi) = 2, and y''(pi) = -1.

(1) What is the value of c1?
(1) What is the value of c2?
(1) What is the value of c3?

I can't figure this one out for nothing!

0=c1+c2cos(pi)+c3sin(pi)
0=c1+c2(-1)+c3(0)
0=c1-c2

2=c1+c2(-sin(pi))+c3(cos(pi))
2=c1+c2(0)-c3

-1=c1+c2(cos(pi))+c3(-sin(pi))
-1=c1-c2

How would I solve the three equations to find each? I'm stuck here

2. Originally Posted by latavee
y = c1 + c2cos x + c3sin x is the general solution of the differential equation y''' + y' = 0 on (-infinity, infinity). Find a member of the family that is a solution with initial conditions y(pi) = 0, y'(pi) = 2, and y''(pi) = -1.

(1) What is the value of c1?
(1) What is the value of c2?
(1) What is the value of c3?

I can't figure this one out for nothing!

0=c1+c2cos(pi)+c3sin(pi)
0=c1+c2(-1)+c3(0)
0=c1-c2

2=c1+c2(-sin(pi))+c3(cos(pi))
2=c1+c2(0)-c3

-1=c1+c2(cos(pi))+c3(-sin(pi))
-1=c1-c2

How would I solve the three equations to find each? I'm stuck here
$y(x)=c_1+c_2 \cos(x)+c_3\sin(x)$

$y'(x)=-c_2\sin(x)+c_3\cos(x)$

$y''(x)=-c_2\cos(x)-c_3\sin(x)$

CB