State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 7y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. an(x) any an-ly +...+ n- dxn 1(x) dxn-1 + a₂₁ (x) dx + a₁(x) = g(x) (6) dx linear O nonlinear

State the order of the given ordinary differential equation. (1-x)y" - 4xy' + 7y = cos x Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. an(x) any an-ly +...+ n- dxn 1(x) dxn-1 + a₂₁ (x) dx + a₁(x) = g(x) (6) dx linear O nonlinear

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Dimensional homogeneity

The term dimensional homogeneity means that in an equation, the dimensions of each term on both sides are equal, which means the dimensions of the left-hand side (LHS) of an equation are similar to the dimensions of the right-hand side (RHS). For a dimensionally homogeneous equation, the powers of fundamental dimensions will be identical on both sides of the equation.

Question

State the order of the given ordinary differential equation.
(1 x)y" - 4xy' + 7y = cos x
Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1.
dny
an(x) + a
dxn
²n-1(x)_
d-ly
+ ... + a₁ (x) -
dxn-1
dx
- 2₁ (x) dy +
+ a(x) y = g(x) (6)
linear
O nonlinear

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