Solve the equation separable, linear, bernoulli, or homogenous1.dydx=x4+4xy22x3+x2y+y32.(e−ycos⁡(x))y′=x4+6x2y33.y′=y+yx3x+x2cos⁡(x2y2)

Quentin Johnson

Quentin Johnson

Answered

2022-01-22

Solve the equation separable, linear, bernoulli, or homogenous
1.dydx=x4+4xy22x3+x2y+y3
2.(eycos(x))y=x4+6x2y3
3.y=y+yx3x+x2cos(x2y2)

Answer & Explanation

Hector Roberts

Hector Roberts

Expert

2022-01-22Added 31 answers

Separable equation:
A first order differential equation y’=f(x,y) is called a separable equation if the function f(x,y) can be factored into the product of two functions of x and y
f(x,y)=f1(x)f2(y)
where f1(x) and f2(y) are continuous functions.
Linear differential equation:
A first order differential equation is linear when it can be written as:
dydx+P(x)y=Q(x)
Where P(x) and Q(x) are functions of x.
Bernoulli differential equation:
A first order Bernoulli differential equation can be written as: dydx+P(x)y=Q(x)
Where P(x) and Q(x) are functions of x.
Bernoulli differential equation:
A first order Bernoulli differential equation can be written as: dydx+P(x)y=Q(x)yn
Where P(x) and Q(x) are functions of x.
Homogeneous differential equation:
A first order homogeneous differential equation can be written as: dydx=F(yx)
All three equations are written in the table :
\[\begin{array}{|c|c|}\hline Equation & Separable & Linear & Bernoilli & Homogeneous\ \hline \frac{dy}{dx}=\frac{x^4+4xy^2}{2x^3+x^2y+y^3} & no & no & no & no\\hline (e^{-y}\cos(x))y=x^4+6x^2y^3

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