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Determine the order of the given différential equation and state whether
the equation is linear or nonlinear.
(a) The order of this differential equation is
(b) The equation is Choose

Ask by Park Reeves. in the United States
Mar 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

(a) The order of the differential equation is 1.
(b) The equation is nonlinear.

Solution

Step 1: Determine the Order
The order of a differential equation is defined by the highest derivative in the equation. In the given equation
the highest derivative present is , which is a first derivative. Therefore, the order is .
Step 2: Check for Linearity
A differential equation is linear if it can be written in the form
where , , and are functions of the independent variable only.
In the given equation
the term contains , which is a nonlinear function of . Since the equation includes a power of greater than , it is nonlinear.
Final Answers:
(a) The order of the differential equation is .
(b) The equation is nonlinear.

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Beyond the Answer

The order of the given differential equation is 1, as it involves only the first derivative of with respect to .
The equation is nonlinear because the term contains raised to a power greater than one, which makes it non-linear in nature.

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