Is the back of the book wrong? Solving a Differential Equation with Cosh(x)

In summary, a differential equation is a mathematical equation that describes the relationship between a function and its derivatives. They are important because they allow us to model and predict the behavior of complex systems in various fields. There are different methods for solving them, and they have applications in physics, biology, engineering, and other fields. There are also software and tools available for solving differential equations, such as Mathematica, MATLAB, and Wolfram Alpha. These tools make it easier to handle complex equations and visualize solutions.
  • #1
Sparky_
227
5

Homework Statement



Solve : y'' -y = cosh(x)


Homework Equations





The Attempt at a Solution



the attempt is attached.

The answer in the back of the book agree with part of mine. However, the circled part - the part with 1/8 as a coefficient on e^x terms. It's circled on the bottom.

Either the back of the book is wrong (and I'm correct) or this term should cancel and I've missed something.
Help?

Thanks
-Sparky_
 

Attachments

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  • #2
The circled term is a solution to the homogeneous equation y''-y=0. It can be absorbed into the c1*exp(x)+c2*exp(-x).
 

FAQ: Is the back of the book wrong? Solving a Differential Equation with Cosh(x)

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many physical phenomena and is an important tool in various fields of science and engineering.

Why are differential equations important?

Differential equations are important because they allow us to model and predict the behavior of complex systems. They are used in physics, biology, engineering, and many other fields to understand and solve real-world problems.

How do you solve a differential equation?

There are different methods for solving differential equations, depending on the type of equation and the initial conditions. Some common techniques include separation of variables, substitution, and using integrating factors.

What are the applications of differential equations?

Differential equations have many applications in various fields, including physics, chemistry, biology, economics, and engineering. They are used to model and understand a wide range of phenomena, such as population growth, chemical reactions, and electrical circuits.

Are there any software or tools available for solving differential equations?

Yes, there are many software and tools available for solving differential equations. Some popular ones include Mathematica, MATLAB, and Wolfram Alpha. These tools can handle complex equations and provide visualizations of the solutions, making it easier to understand and analyze the results.

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