An equation of the form is called a Riccati equation. (a) If p(x) 0 show that the equation is linear. If r(z) 0 show that it is a Bernoulli equation. (b) If y = n(x) is some particular solution, show that the change of variable y = y(x) + leads to a linear equation in u.

An equation of the form is called a Riccati equation. (a) If p(x) 0 show that the equation is linear. If r(z) 0 show that it is a Bernoulli equation. (b) If y = n(x) is some particular solution, show that the change of variable y = y(x) + leads to a linear equation in u.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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(6) An equation of the form
is called a Riccati equation.
(a) If p(r) 0 show that the equation is linear. If r(z) 0 show that it is a Bernoulli equation.
(b) If y = m(x) is some particular solution, show that the change of variable y = y(2) + leads to a
linear equation in u.

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