Determine the order of the given differential equation state whether the equation is linear or...

Question:

Determine the order of the given differential equation state whether the equation is linear or nonlinear.

{eq}(a) t^2 (d^2 y/dt^2) + t (dy/dt) + 2y = sin t \\ (b) (1 + y^2) (d^2 y/dt^2) + t (dy/dt) + y = e^t \\ (c) d^4 y/dt^4 + d^3 y/dt^3 + d^2 y/dt^2 + dy/dt + y = 1 \\ {/eq}

Order and degree of differential equations

Order of differential equations is the maximum power raised to any derivative equation for a given differential equation. The degree of a differential equation is equal to the power raised in the derivative having maximum power raised for a given differential equation.

Answer and Explanation:

Order Order of differential equations is the maximum power raised to any derivative equation for a given differential equation.

DegreeThe degree of a differential equation is equal to the power raised in the derivative having maximum power raised for a given differential equation.

(A)

This equation has order 2 and degree 1 thus; this is second order linear differential equation.

(B)

This equation has order 2 and degree 1 thus; this is second order linear differential equation.

(A)

This equation has order 4 and degree 1 thus; this is fourth order linear differential equation.


Learn more about this topic:

Loading...
Basic Calculus: Rules & Formulas

from Calculus: Tutoring Solution

Chapter 3 / Lesson 6
57K

Related to this Question

Explore our homework questions and answers library