My book says the general form of a linear differential

Nyah Conrad

Nyah Conrad

Answered question

2022-02-15

My book says the general form of a linear differential equation is:
y+P(x)y=Q(x)
But my teacher said that a linear differential equation has the general form:
y+P(x)y+Q(x)y=f(x)
Which is the correct form or they are both correct?

Answer & Explanation

par5o4nr4z

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(n)+j=0n1Pj(x)y(j)=f(x),
where
y(j)=(ddx)jy
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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