Question
Asked Nov 11, 2019
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Find the function F that satisfies the following differential equations and initial conditions.

F''(x)=cos x, F'(0)=3, F(pi)=5

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Expert Answer

Step 1

Given that,

(1) f\'\'(x)=cos x

(2) f\'(0)=3

(3)f(π)=5

 

Integrate equation 1;

...
f (x)sinx)c ...4)
Using criteria (2);
f(0) sin(0)c
3 0C
C3
Equation (4) is re written as,
f (x) sin(x)3..5)
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Image Transcriptionclose

f (x)sinx)c ...4) Using criteria (2); f(0) sin(0)c 3 0C C3 Equation (4) is re written as, f (x) sin(x)3..5)

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Tagged in

Math

Calculus

Derivative