The differential equation $y ^ { \prime \prime \prime } + 2 y ^ { \prime \prime } + 3 x y ^ { \prime } - 4 e ^ { x } y = \sin x$ is
A) first order linear
B) second order linear
C) third order linear
D) first order nonlinear
E) second order nonlinear

Question

Quizplus · Accepted Answer

This differential equation is third order because the highest derivative is $y^{\prime\prime\prime}$ (third derivative of y). It is linear because the equation is a linear combination of the function y and its derivatives, without any products or nonlinear functions of y and its derivatives.

The Differential Equation y′′′+2y′′+3xy′−4exy=sin⁡xy ^ { \prime \prime \prime } + 2 y ^ { \prime \prime } + 3 x y ^ { \prime } - 4 e ^ { x } y = \sin xy′′′+2y′′+3xy′−4exy=sinx

The Differential Equation $y ^ { \prime \prime \prime } + 2 y ^ { \prime \prime } + 3 x y ^ { \prime } - 4 e ^ { x } y = \sin x$