Substitutions at bernoulli equations, Mathematics

Assignment Help:

In the prior section we looked at Bernoulli Equations and noticed that in order to solve them we required to use the substitution v = y1-n. By using this substitution we were capable to convert the differential equation in a form which we could deal along with but, linear in this case. In this section we need to see a couple of other substitutions which can be used to reduce several differential equations down to a solvable form.

The first substitution we'll take a seem at will need the differential equation to be in the create,

y' = F(y/x)

First order differential equations which can be written in this form are termed as homogeneous differential equations. Remember that we will generally have to do several rewriting in order to place the differential equation in the exact form.

Once we have verified as the differential equation is a homogeneous differential equation and we've gotten this written in the exact form we will use the subsequent substitution.

n (x) = y/x

We can then rewrite this as,

 y = xn

 And after that remembering that both y and v are functions of x we can utilize the product rule to calculate,

y′ = n + xn′

In this substitution the differential equation is like,

n + xn′ = F(n)

⇒ xn′ = F(n) - n

⇒ dv/ F(v) - v = dx/x

When we can notice with a small rewrite of the new differential equation we will have a separable differential equation after the substitution.


Related Discussions:- Substitutions at bernoulli equations

Multiplication of two like terms with same signs, Case 1: Suppose we...

Case 1: Suppose we have two terms 7ab and 3ab. When we multiply these two terms, we get 7ab x 3ab = (7 x 3) a 1 + 1 . b 1 + 1  ( Therefore, x m . x n = x m +

I need help with my homework.., Uh on my homework it says 6m = $5.76 and I ...

Uh on my homework it says 6m = $5.76 and I dont get it..

Fraction, in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are ...

in a garden 1/8 of the flowers are tulips. 1/4 of the tulips are rd. what fraction of the flowers in the garden are red tulips

Basic indefinite integrals- computing indefinite integrals, Basic indefinit...

Basic indefinite integrals The first integral which we'll look at is the integral of a power of x.                                ∫x n dx = (x n +1 / n + 1)+ c,          n

Expected value, Expected Value For taking decisions under conditions of...

Expected Value For taking decisions under conditions of uncertainty, the concept of expected value of a random variable is used. The expected value is the mean of a probability

Interpretations of definite integral, Interpretations of Definite Integral ...

Interpretations of Definite Integral There are some quick interpretations of the definite integral which we can give here. Firstly, one possible interpretation of the defini

Descriptive statistics, Descriptive Statistics Statistics Definit...

Descriptive Statistics Statistics Definition of Statistics: it viewed as a subject is a process of tabulating, collecting and analyzing numerical data upon which importan

Green function, greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t...

greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s

Trignometry, verify 4(sin^4 30^0+cos60^0 )-3(cos^2 ?45?^0-sin^2 90^0 )=2

verify 4(sin^4 30^0+cos60^0 )-3(cos^2 ?45?^0-sin^2 90^0 )=2

Equal matrices, Is this given matrices are called equal Matrices?

Is this given matrices are called equal Matrices?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd