Solve the initial value problem. \frac{d^2y}{dx^2} = 4 \sec^2 x; y'(\frac {\pi}{4}) = 0; y(0) = 0...

Question:

Solve the initial value problem.

{eq}\frac{d^2y}{dx^2} = 4 \sec^2 x;~y'(\frac {\pi}{4}) = 0;~y(0) = 0 {/eq}

The solution is {eq}y = {/eq}

(Type an exact answer, using {eq}\pi {/eq} as needed.)

Initial Value Problem:


With the help of the indefinite integration, we can find the {eq}(m-1)^{th} {/eq} order derivative by integrating the {eq}m^{th} {/eq} order derivative. For example, we can obtain {eq}f'(x)+C {/eq} on integrating {eq}\displaystyle\int f''(x)\ \text dx. {/eq} The result will contain an arbitrary constant which can be easily eliminated by plugging the given initial conditions.

Answer and Explanation: 1

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Given equation: {eq}\dfrac{d^2y}{dx^2} = 4 \sec^2 x\Rightarrow y''(x)=4\sec^2 x {/eq}

Now, we will integrate both sides using the rule...

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Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.


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