State the order of the differential equation and indicate if it is linear or nonlinear.
$y^{$\prime$}$\bullet$ y=3e^{t}$

$1^{st}$ order, linear

$1^{st}$ order, nonlinear

$2^{nd}$ order, linear

$2^{nd}$ order, nonlinear

Verified step by step guidance

Identify the order of the differential equation by determining the highest derivative of the dependent variable (y) present in the equation. In this case, the equation involves y′ (the first derivative of y), so it is a first-order differential equation.

To determine if the equation is linear or nonlinear, recall that a differential equation is linear if the dependent variable (y) and all its derivatives appear to the first power and are not multiplied by each other. Otherwise, it is nonlinear.

Examine the given equation: y′∙y = 3e^t. Here, y′ (the first derivative) is multiplied by y (the dependent variable), which violates the condition for linearity. Therefore, the equation is nonlinear.

Summarize the findings: The equation is a first-order (1st order) differential equation because the highest derivative is y′, and it is nonlinear because y′ and y are multiplied together.

Conclude that the correct classification of the differential equation is: 1st order, nonlinear.

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State the order of the differential equation and indicate if it is linear or nonlinear. y′∙y=3ety^{\(\prime\)}\(\bullet\) y=3e^{t}y′∙y=3et

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State the order of the differential equation and indicate if it is linear or nonlinear.
$y^{\(\prime\)}\(\bullet\) y=3e^{t}$