*Furthermore, the left-hand side of the equation is the derivative of \(y\).*

*Furthermore, the left-hand side of the equation is the derivative of \(y\).*

It can be shown that any solution of this differential equation must be of the form \(y=x^2 C\).

This is an example of a general solution to a differential equation.

One such function is \(y=x^3\), so this function is considered a is an equation involving an unknown function \(y=f(x)\) and one or more of its derivatives.

A solution to a differential equation is a function \(y=f(x)\) that satisfies the differential equation when \(f\) and its derivatives are substituted into the equation. Note that a solution to a differential equation is not necessarily unique, primarily because the derivative of a constant is zero.

Consider the equation \(y′=3x^2,\) which is an example of a differential equation because it includes a derivative.

There is a relationship between the variables \(x\) and \(y:y\) is an unknown function of \(x\).

In fact, any function of the form \(y=x^2 C\), where \(C\) represents any constant, is a solution as well.

The reason is that the derivative of \(x^2 C\) is \(2x\), regardless of the value of \(C\).

Calculus is the mathematics of change, and rates of change are expressed by derivatives.

Thus, one of the most common ways to use calculus is to set up an equation containing an unknown function \(y=f(x)\) and its derivative, known as a differential equation.

## Comments Solved Problems In Differential Equations

## Homogeneous Differential Equations - Math Is Fun

Here we look at a special method for solving "Homogeneous Differential Equations" Homogeneous Differential Equations. A first order Differential Equation is Homogeneous when it can be in this form dy dx = F y x We can solve it using Separation of Variables but first we create a new variable v = y x…

## Separable differential equations Calculator & Solver - Snapxam

Separable differential equations Calculator online with solution and steps. Detailed step by step solutions to your Separable differential equations problems online with our math solver and calculator. Solved exercises of Separable differential equations.…

## Differential Equations - Introduction - Math Is Fun

We solve it when we discover the function y or set of functions y. There are many "tricks" to solving Differential Equations if they can be solved. And how powerful mathematics is! That short equation says "the rate of change of the population over time equals the growth rate times the.…

## Differential Equation Calculator - eMathHelp

Differential Equations Calculators; Math Problem Solver all calculators Differential Equation Calculator. The calculator will find the solution of the given ODE first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. Initial conditions are also supported.…

## Part 1 Mixing Problems with Differential Equations - YouTube

Part one of a two video series on a mixing problem.…

## Ordinary Differential Equations Calculator - Symbolab

Advanced Math Solutions – Ordinary Differential Equations Calculator, Exact Differential Equations In the previous posts, we have covered three types of ordinary differential equations, ODE. We have now reached.…

## Differential equations introduction video Khan Academy

So the solution here, so the solution to a differential equation is a function, or a set of functions, or a class of functions. It's important to contrast this relative to a traditional equation. So let me write that down. So a traditional equation, maybe I shouldn't say traditional equation, differential equations have been around for a while.…

## Differential Equations -

Differential Equations. Differential equations are a special type of integration problem. Here is a simple differential equation of the type that we met earlier in the Integration chapter `dy/dx=x^2-3` We didn't call it a differential equation before, but it is one. We'll see several different types of differential equations in this chapter.…