Nyah Conrad

2022-02-15

My book says the general form of a linear differential equation is:

${y}^{\prime}+P\left(x\right)y=Q\left(x\right)$

But my teacher said that a linear differential equation has the general form:

$y{}^{\u2033}+P\left(x\right){y}^{\prime}+Q\left(x\right)y=f\left(x\right)$

Which is the correct form or they are both correct?

But my teacher said that a linear differential equation has the general form:

Which is the correct form or they are both correct?

par5o4nr4z

Beginner2022-02-16Added 5 answers

Both are linear differential equations. To be more general, the general form of an order n linear differential equation is

${y}^{\left(n\right)}+\sum _{j=0}^{n-1}{P}_{j}\left(x\right){y}^{\left(j\right)}=f\left(x\right)$ ,

where

${y}^{\left(j\right)}={\left(\frac{d}{dx}\right)}^{j}y$

is the jth derivative of y. In this terminology, your book gave the most general first order linear differential equation, and your teacher gave general second order linear differential equation.

where

is the jth derivative of y. In this terminology, your book gave the most general first order linear differential equation, and your teacher gave general second order linear differential equation.

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