Aryan Emery

2022-02-24

Define what linear first-order equation forms?

Mikayla Swan

Beginner2022-02-25Added 9 answers

Linear differential equation:

a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

${a}_{0}\left(x\right)y+{a}_{1}\left(x\right){y}^{\prime}+{a}_{2}\left(x\right)y{}^{\u2033}+\dots +{a}_{n}\left(x\right){y}^{\left(n\right)}+b\left(x\right)=0$ ,

where${a}_{0}\left(x\right),\dots {a}_{n}\left(x\right)$ and $b\left(x\right)$ are arbitrary differentiable functions that do not need to be linear, and $y}_{1}^{\prime},\dots ,{y}^{\left(n\right)$ are the successive derivatives of an unknown function y of the variable x.

This is an ordinary differentiable function (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives.

linear first-order equation forms

$\frac{dy}{dx}+Py=Q$

Where P and Q are functions of x.

This is the required form.

a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

where

This is an ordinary differentiable function (ODE). A linear differential equation may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives.

linear first-order equation forms

Where P and Q are functions of x.

This is the required form.

Donald Erickson

Beginner2022-02-26Added 8 answers

Thanks!

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?

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