# Determine the function y= f(x) such that {eq}y'= \frac{1}{10}y\ and\ f(0)= -3. {/eq}

## Question:

Determine the function y= f(x) such that {eq}y'= \frac{1}{10}y\ and\ f(0)= -3. {/eq}

## Initial Value Problem:

The initial value problem is given in the form of an ordinary differential equation {eq}\ y' = f(t,y). \ {/eq} To solve an initial value problem we have to integrate the equation by taking same variables on a particular side.This gives the general solution of the given differential equation. Then with the help given condition we determine the value of integral constant which then gives the particular solution of the given differential equation.

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Given:

{eq}\displaystyle { y'= \frac{1}{10}y } {/eq}

Rewriting the equation as:

{eq}\displaystyle { \frac{dy}{dx}= \frac{1}{10}y \\...

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.