# Horrible expression involving logs and inverse tan functions

• coverband
In summary, a "horrible expression" involving logs and inverse tan functions is a complex mathematical equation that can be difficult to simplify or solve without a calculator or computer. These functions are often considered difficult to work with because they involve complex concepts and often require the use of technology. However, they are commonly used in scientific calculations to help solve complex equations and model natural phenomena. To solve a "horrible expression," one must use a combination of algebraic manipulation and logarithm/trigonometric identities, and sometimes a calculator or computer. Furthermore, these types of expressions have real-world applications in fields such as science and engineering, where they can be used to model and predict various phenomena.
coverband

## Homework Statement

$$\frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0$$

## Homework Equations

$$\frac{dy}{dx} + (y^4-1) = 0$$

## The Attempt at a Solution

$$\frac{dy}{dx} = (1- y^4)$$
$$\frac{dy}{1- y^4} = dx$$

Then I get a horrible expression involving logs and inverse tan functions on the LHS and x + A on RHS ?

sorry heading should be ODE not PDE

Last edited by a moderator:

You have the wrong expression after the integration, try taking the derivative of that with respect to x to see if you get the same expression as you started with. HINT: You forgot the x to y dependence.

## 1. What is a "horrible expression" involving logs and inverse tan functions?

A "horrible expression" in this context is a complicated mathematical equation that involves logarithms (logs) and the inverse tangent function (tan-1). It may be difficult to simplify or solve without using a calculator or computer.

## 2. Why are logs and inverse tan functions often considered difficult to work with?

Logs and inverse tan functions are considered difficult because they involve complex mathematical concepts, such as exponents and trigonometry. They also often require the use of a calculator or computer to solve.

## 3. What is the purpose of using logs and inverse tan functions in scientific calculations?

Logs and inverse tan functions are used in scientific calculations to help simplify and solve complex equations. They are also commonly used in fields such as physics, engineering, and astronomy to model and understand natural phenomena.

## 4. How do you solve a "horrible expression" involving logs and inverse tan functions?

Solving a "horrible expression" involving logs and inverse tan functions usually requires a combination of algebraic manipulation and the use of logarithm and trigonometric identities. It may also involve using a calculator or computer to find an approximate solution.

## 5. Can "horrible expressions" involving logs and inverse tan functions have real-world applications?

Yes, "horrible expressions" involving logs and inverse tan functions can have real-world applications in various fields of science and engineering. For example, they can be used to model the spread of diseases, predict the behavior of complex systems, and calculate the trajectories of objects in motion.

Replies
3
Views
809
Replies
15
Views
1K
Replies
6
Views
1K
Replies
4
Views
874
Replies
1
Views
1K
Replies
6
Views
1K
Replies
2
Views
975
Replies
21
Views
1K
Replies
3
Views
1K
Replies
2
Views
722