Asked Oct 3, 2019

Find f if f''(x)=2+cos(x), f(0)=−2, f(pi/2)=6

f(x)= ?


Expert Answer

Step 1

Please see the white board. C1 is the constant of integration.


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dy = 2 + cosx " (ar)da - e+ dy cosx)dx = 2x + sinx + C (2 dx

Step 2

We need to integration the expression one more time to get the final answer. Please see the white board.


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dy (2ax sinxCi)dx f(x)2 cosaC1C2

Step 3

When x = 0; f(0) = -2

Hence, 02 - cos0 + C1 x 0 + C2 = C2 - 1 = -2

Hence, C2 = 1 - 2 = -1

Hence, f(x...

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Differential Equations

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