Mathematics, 17.01.2020 00:31 simonthang8

Determine whether each first-order differential equation is separable, linear, both, or neither. 1. +=x2y2 2. y+sinx=x3y′ 3. lnx−x2y=xy′ 4. +cosy=tanx

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Answer from: Laylahlettiere

a) Linear

b) Linear

c) Linear

d) Neither

See explanation below.

Step-by-step explanation:

a) $\frac{dy}{dx} +e^x y = x^2 y^2$

For this case the differential equation have the following general form:

y' +p(x) y = q(x) y^n

Where p(x) =e^x and q(x) = x^2 and since n>1 we can see that is a linear differential equation.

b) y + sin x = x^3 y'

We can rewrite the following equation on this way:

$y' -\frac{1}{x^3} y= \frac{sin (x)}{x^3}$

For this case the differential equation have the following general form:

y' +p(x) y = q(x) y^n

Where $p(x) =-\frac{1}{x^3}$ and $q(x) = \frac{sin(x)}{x^3}$ and since n=0 we can see that is a linear differential equation.

c) ln x -x^2 y =xy'

For this case we can write the differential equation on this way:

$y' +xy = \frac{ln(x)}{x}$

For this case the differential equation have the following general form:

y' +p(x) y = q(x) y^n

Where p(x) =x and $q(x) = \frac{ln(x)}{x}$ and since n=0 we can see that is a linear differential equation.

d) $\frac{dy}{dx} + cos y = tan x$

For this case we can't express the differential equation in terms:

y' +p(x) y = q(x) y^n

So the is not linear, and since we can separate the variables in order to integrate is not separable. So then the answer for this one is neither.

Answer from: Quest

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

Answer from: Quest

answer

step-by-step explanation:

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Determine whether each first-order differential equation is separable, linear, both, or neither. 1....

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