Find {eq}f(x) {/eq} if {eq}f''(x) = 3e^x + 5 \sin x {/eq}, {eq}f(0) = 1 {/eq}, and {eq}f'(0) = 2 {/eq}.

Question:

Find {eq}f(x) {/eq} if {eq}f''(x) = 3e^x + 5 \sin x {/eq}, {eq}f(0) = 1 {/eq}, and {eq}f'(0) = 2 {/eq}.

Initial Value Problems:

Initial conditions are a condition or a set of conditions on the solution that allow us to determine which solution that we are focused on. An initial value problem (IVP) is a differential equation along with a number of given initial conditions.

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To find {eq}f'(x), {/eq} we integrate {eq}f''(x), {/eq} that is, $$f'(x) =\displaystyle\int f''(x) dx = \int 3e^x + 5\sin x dx= 3e^x - 5\cos x...

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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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