Solve the differential equation y double prime - 10y prime + 25y = 0 with the initial conditions:...

Question:

Solve the differential equation {eq}{y}''- 10{y}' + 25y = 0 {/eq} with the initial conditions: when{eq}x = 0, y = 1 {/eq} and when {eq}x = 0, {y}' = 1 {/eq}.

A) Find the general solution.

B) Find the particular solution using the given initial conditions.

C) Sketch the graph. Use the windows {eq}[-2, 1], \, [-2, 2] {/eq}.

Initial value problem:


The initial value problem is the differential equation with some initial conditions. The differential equation is the equation which contains one or more functions and their derivatives.

Answer and Explanation: 1

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Given:


  • The given differential equation is, {eq}y'' - 10y' + 25y = 0 {/eq} and the initial conditions are {eq}y\left( 0 \right) = 1 {/eq} and...

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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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