I need to know whether there is some

Cash Duncan

Cash Duncan

Answered question

2022-04-06

I need to know whether there is some theorem that states that solutions to differential equations of the form
dnydtn+dn1ydtn1gn1(t)++dydtg1(t)+y=go(t)

Answer & Explanation

Marin Lowe

Marin Lowe

Beginner2022-04-07Added 18 answers

Step 1
Basically you want the multivariate version of the Existence and Uniqueness Theorem for differential equations. Your equation can be put in the form
Y=F(Y,t)
where Y(t)=(y(t),y(t),,y(n1)(t)) and
F(Y,t)=(Y2,Y3,,Yn,gn1(t)Yng1(t)Y2Y1+g0(t))

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