# Simple differential equation

• seto6
In summary, the person is asking for help in solving a differential equation and is wondering if they have given the correct equation. They also suggest trying solutions of the form y = a xb or y = m xn + k.
seto6

## Homework Statement

solve the following differential equation
(y')2 +x3y'-2x2y=0

non

## The Attempt at a Solution

i can't seem to find any way to solve it...
could someone give me a hint pls.!

Some misleading title you have there: "simple differential equation..." :)

seto6 said:

## Homework Statement

solve the following differential equation
(y')2 +x3y'-2x2y=0

non

## The Attempt at a Solution

i can't seem to find any way to solve it...
could someone give me a hint pls.!

You're sure that you have given us the correct differential equation, right?

If it were y'2 + xy' - 2x2y = 0, you could factor it into (y' + 2xy1/2)(y - xy1/2) = 0, and you could solve each one separately.

Or if you had y'2 + x3y' + 2x2y = 0, you could write this as y'2 + d/dx(x3y) = 0. I'm not sure what you could do with that, though.

I seem to find a solution of the form y = a xb, so try that. There's another of the form y = m xn + k too.

Last edited:

## What is a simple differential equation?

A simple differential equation is an equation that involves a function and its derivatives, and is used to model the relationship between a quantity and its rate of change over time.

## What are the basic components of a simple differential equation?

The basic components of a simple differential equation are the dependent variable, the independent variable, and the derivative of the dependent variable with respect to the independent variable.

## What is the purpose of solving a simple differential equation?

The purpose of solving a simple differential equation is to find the functional relationship between the dependent and independent variables, and to predict the behavior of the dependent variable over time.

## What are the different methods for solving a simple differential equation?

There are several methods for solving a simple differential equation, including separation of variables, substitution, and the use of integrating factors.

## What are some real-life applications of simple differential equations?

Simple differential equations are used in various fields such as physics, engineering, economics, and biology to model and analyze natural phenomena and predict their behavior over time. Examples include population growth, radioactive decay, and electrical circuits.

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