Toronto Math Forum

APM346-2021S => APM346--Tests & Quizzes => Quiz 1 => Topic started by: Gavrilo Milanov Dzombeta on January 29, 2021, 10:34:47 AM

Title: Quiz 1 - Variant 2E - Problem 1
Post by: Gavrilo Milanov Dzombeta on January 29, 2021, 10:34:47 AM
Consider first order equations and determine if they are linear homogeneous, linear inhomogeneous, or nonlinear ($u$ is an unknown function); for nonlinear equations, indicate if they are also semilinear or quasilinear:
$$u_t +u^2_x + u^2_y = 0.  $$
$$\text{The equation is nonlinear homogeneous}$$
Title: Re: Quiz 1 - Variant 2E - Problem 1
Post by: Victor Ivrii on January 29, 2021, 11:41:45 AM
Indeed, this equation has $u=0$ as a solution but the notion of "homogeneou"s does not apply to nonlinear.