The method of undetermined coefficients can sometimes be used to solve first-order ordinary differential equations. Use the method to solve the following equations. y'-3y=5e^{3x}

Josalynn

Josalynn

Answered question

2021-05-19

The method of undetermined coefficients can sometimes be used to solve first-order ordinary differential equations. Use the method to solve the following equations.
y3y=5e3x

Answer & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-05-20Added 98 answers

Step 1
The differential equation is y3y=5e3x
Using the method of undetermined coefficient, the solution of the equation will be of the form y=yh+yp where yh is the general solution to the corresponding homogeneous equation and yp is the particular solution.
Find the general solution to y3y=0.
The characteristic equation is r3=0.
r3=0
r=3
Thus, the general solution is, yh=c1e3x.
Step 2
To find the particular solution, suppose yp=Axe3x.
yp=3Axe3x3Axe3x=5e3x
Ae3x=5e3x
A=5
Thus, the particular solution is yp=5xe3x.
Therefore, the solution of the equation is,
y=yh+yp
=c1e3x+5xe3x
That is, y=c1e3x+5xe3x.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-19Added 2605 answers

Answer is given below (on video)

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