### Solving Differential Equations with Independent Variable xTo solve the given third-order differential equation with $ x $ as the independent variable, follow the steps below:#### Differential Equation\[ y''' - 3y'' - 40y' = 0 \]Find a general solution for this differential equation.#### General SolutionA general solution expressed with $ x $ as the independent variable can be denoted as $ y(x) $. To solve this, you'll typically use methods involving characteristic equations for ordinary differential equations.The textbox where the solution should be input is denoted as:\[ y(x) = \_\_\_\_\_\_\_\_ \]Be sure to follow the method appropriate for solving third-order linear ordinary differential equations.For further learning and a step-by-step guide, refer to our tutorials and examples section on solving higher-order differential equations.

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Find a general solution for the given differential equation with x as the independent variable. у" - Зу" - 40y' 3D0

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.4: Solving Nonlinear Equations

Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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### Solving Differential Equations with Independent Variable x

To solve the given third-order differential equation with $ x $ as the independent variable, follow the steps below:

#### Differential Equation
\[ y''' - 3y'' - 40y' = 0 \]

Find a general solution for this differential equation.

#### General Solution
A general solution expressed with $ x $ as the independent variable can be denoted as $ y(x) $. To solve this, you'll typically use methods involving characteristic equations for ordinary differential equations.

The textbox where the solution should be input is denoted as:
\[ y(x) = \_\_\_\_\_\_\_\_ \]

Be sure to follow the method appropriate for solving third-order linear ordinary differential equations.

For further learning and a step-by-step guide, refer to our tutorials and examples section on solving higher-order differential equations.

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