Determine the order of the given partial differential equation; also

jernplate8

jernplate8

Answered question

2021-10-04

Determine the order of the given partial differential equation; also state whether the equation is linear or nonlinear.
52ux+ut=1+u×

Answer & Explanation

casincal

casincal

Skilled2021-10-05Added 82 answers

Step 1
The given partial differential equation is 52ux+ut=1+u×.
Step 2
The order of the partial differential equation is the order of the highest derivative in that equation.
In the given partial differential equation, the highest derivative is u×.
The order of highest derivative u× is 2.
So, the order of the partial differential equation 52ux+ut=1+u×.
Step 3
Now determine whether the equation is linear or non linear as follows.
The given equation is 52ux+ut=1+u×.
Here, the degrees of the partial derivatives ux,ut and u× are one.
That is, the partial derivatives in the equation occurs linearly.
A partial differential equation in which the degree of dependent variable and its partial derivatives are at most one is said to be linear partial differential equation.
So, the equation 52ux+ut=1+u× is linear.
Hence, the equation 52ux+ut=1+u× is a second order linear partial differential equation.

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