Label each of the following as linear, separable, or both;dy3x2 – ydxdy – 5y³ = 0dxdy+ 3x²y = 0dx

Answered: Label each of the following as linear,…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Step 1

A differential equation is linear only if it satisfies the conditions below.

The degree of the differential equation is 1 .
The exponent of each differential quotient is 1.
The exponent of the dependent variable is equal to 1.
There should not be any term that contains the product of the differential quotient and the dependent variable.
There should not be any term that contains the product of the differential quotients.
Neither dependent variable nor differential coefficient is in transcendental form.

If any of the above conditions is not satisfied, then the differential equation is not linear.

A differential equation is separable, if the terms with the like variables can be isolated on either sides of an equation.