Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q2.6-4E

Expert-verified
Fundamentals Of Differential Equations And Boundary Value Problems
Found in: Page 76
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

In problems 1-8 identify (do not solve) the equation as homogeneous, Bernoulli, linear coefficients, or of the form y'=G(ax+by). (t+x+2)dx+(3t-x-6)dt=0

The given equation is the form of linear coefficients.

See the step by step solution

Step by Step Solution

General form of homogeneous, Bernoulli, linear coefficients of the form of y'=Gax+by

  • Homogeneous equation

If the right-hand side of the equation dydx=fx,ycan be expressed as a function of the ratio yxalone, then we say the equation is homogeneous.

Equations of the form dydx=Gax+by

When the right-hand side of the equation dydx=fx,ycan be expressed as a function of the combination ax+by, where a and b are constants, that is, dydx=Gax+by then the substitution z=ax+by transforms the equation into a separable one.

  • Bernoulli’s equation

A first-order equation that can be written in the form dydx+Pxy=Qxyn, where P(x) and Q(x) are continuous on an interval (a,b) and n is a real number, is called a Bernoulli equation.

  • Equation of Linear coefficients

We have used various substitutions for y to transform the original equation into a new equation that we could solve. In some cases, we must transform both x and y into new variables, say u and v. This is the situation for equations with linear coefficients-that is, equations of the form

a1x+b1y+c1dx+a2x+b2y+c2dy=0

Evaluate the given equation

Given,

By evaluating

t+x+2dx+3t-x-6dt=0

Since,

The given equation satisfies a1b2,a2b1

Therefore, the given equation is the form of a linear coefficient.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.