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The solution of initial value problem: \frac{d^2y}{dx^2} + y = 0,\; y(0) = 1,\; \frac{dy}{dx}(0)...

Question:

The solution of initial value problem: {eq}\frac{d^2y}{dx^2} + y = 0,\; y(0) = 1,\; \frac{dy}{dx}(0) = 0 {/eq}.

a) y = coshx

b) y = cosx

c) y = sinhx

d) y = sinx

Initial Value Problem:

In case of initial value problems, usually we have to deal with ordinary ary differential equations along with some combination of initial conditions. Response due to initial conditions is known as natural response.

Answer and Explanation: 1

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Given Data:

{eq}\begin{align*} \dfrac{d^2y}{dx^2} + y &= 0\\[0.3 cm] (D^2+1)y&=0\\[0.3 cm] y(0) &= 1\\[0.3 cm] y'(0)&= 0\\[0.3...

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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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