How do I find a second order differential

dotzis16xd

dotzis16xd

Answered question

2022-03-25

How do I find a second order differential equation given its solution?
Given that y=Aex+Be2xx
Find ay(x)+by(x)+cy=f(x)
I have considered the auxiliary equation whose roots should be the exponents in the given equation: k1=1 and k2=2. I believe that f(x)=px+q given the additional -x term but I don't know how to find the values of a,b or c for the differential equation.

Answer & Explanation

Deon Frost

Deon Frost

Beginner2022-03-26Added 6 answers

Well, you know the roots λ of the auxiliary equation and the order of the DE, which means aλ2+bλ+c=0 has roots 1 and 2. Once you find a,b,c, f(x) can be found by plugging y=x into ay+by+cy.

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