Ordinary Differential Equations (ODEs) Calculator

Ask and get solution to your homeworkAsk now and get step-by-step solutions

Example

Created on 2024-06-20Asked by Victoria Hernandez (Solvelet student)

Solve the ordinary differential equation

\frac{dy}{dx} = y

Solution

To solve the ordinary differential equation

\frac{dy}{dx} = y

, follow these steps: 1. Separate variables:

\frac{dy}{y} = dx.

2. Integrate both sides:

\int \frac{1}{y} \, dy = \int 1 \, dx,

\ln |y| = x + C,

where

C

is the integration constant. 3. Solve for

y

|y| = e^{x+C} = e^C e^x,

y = Ce^x,

where

C = \pm e^C

. Therefore, the general solution to the differential equation is

y = Ce^x

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Olivia Hernandez on Solvelet

1. Solve the initial value problem

y' = 2y

y(0) = 1

, analytically.2. Find the general solution to the differential equation

y'' + 4y' + 4y = 0

DefinitionODEs are equations of the form where we need to be able to take these derivatives, to make sense out of the equation. Derivatives are defined as the rate of change of a quantity and are categorized by order and linearity. Example: dxdy=ky (where k is constant) is a first-order ODE, and describes exponential growth or decay.

Related Calculators

Orthogonal Functions Calculator Boundary Value Problems Calculator Eigenvalue Methods Calculator Place Value Calculator

Need topic explanation ? Get video explanation