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Find the solution of the differential equation that satisfies the given initial condition.

Find the solution of the differential equation that satisfies the given initial condition.

asked Jan 31, 2015 in CALCULUS by anonymous
reshown Jan 31, 2015 by goushi

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1 Answer

Step 1:

The differential equation is .

Rewrite the equation is .

Apply integral on each side.

Apply integration sum rule.

Apply integration rule.

Apply integration power rule .

Apply trigonometric integration rule.

The equation is .

Step 2:

Find constant value.

The condition .

Substitute and in equation .

Substitute in equation .

The equation is .

The condition , then .

.

The solution of differential equation is .

Solution:

The solution of differential equation is .

answered Jan 31, 2015 by Sammi Mentor
edited Jan 31, 2015 by Sammi

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