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

Evaluating a function, Evaluating a Function You evaluate a function by...

Evaluating a Function You evaluate a function by "plugging in a number". For example, to evaluate the function f(x) = 3x 2 + x -5 at x = 10, you plug in a 10 everywhere you

Intercepts, The last topic that we want to discuss in this section is that ...

The last topic that we want to discuss in this section is that of intercepts.  Notice that the graph in the above instance crosses the x-axis in two places & the y-axis in one plac

Linear programming, As office manager of her firm, Marcellyne has been dir...

As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic

Determine an actual explicit solution, Determine an actual explicit solutio...

Determine an actual explicit solution to y′ = t/y; y(2) = -1. Solution : We already identify by the previous illustration that an implicit solution to this IVP is y 2 = t 2 -

Retail price index, Retail price index This is weighted average of pri...

Retail price index This is weighted average of price relatives based on an average household in the base year. The items consumed are divided into groups as liker food, transp

What is the value of x in probability , A bag contains 8 red balls and x bl...

A bag contains 8 red balls and x blue balls, the odd against drawing a blue ball are 2: 5. What is the value of x?                                                               (An

Algebra, sir/madam, i abdulla working as a maths teacher want to join ur es...

sir/madam, i abdulla working as a maths teacher want to join ur esteemed organisation as a tutor how can i proceed i have created an account even pls guide me, thanks abdulla

How many permutations can you make of the word statistics, Q. How many perm...

Q. How many permutations can you make of the word STATISTICS? Solution:  There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'

Percentage of values will fall in the normal group, If the normal range is ...

If the normal range is 65-10 mg/dl, then what percentage of values will fall in the normal group?

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