A nonhomogeneous equation and a particular solution are given. Find a general so

Bergen

Bergen

Answered question

2021-09-19

A nonhomogeneous equation and a particular solution are given. Find a general solution for the equation.
yy=10t,yp(t)=10t
y(t)=?

Answer & Explanation

faldduE

faldduE

Skilled2021-09-20Added 109 answers

Step 1
According to the given information, it is required to find the general solution of the given differential equation whose particular solution is given.
yy=10t,yp(t)=10t
Step 2
The general solution to the non-homogeneous differential equation can be written as:
y(t)=yc(t)+yp(t)
where yc(t) is the solution to homogeneous differential equation
and yp(t) is the particular solution
Step 3
Now, first find the solution to homogeneous differential equation.
characteristic equation:
r21=0
r2=1
r=±1
yc(t)=c1et+c2et
Step 4
Now, the general solution to differential equation is:
y(t)=yc(t)+yp(t)
=c1et+c2et10t

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