# 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...