partial differential equations - difference between linear, semilinear and quasilinear PDE's - Mathematics Stack Exchange

I know a PDE is linear when the dependent variable $u$ and its derivatives appear only to the first power. So, $u_t + u_x +5u = 1$ would be linear. However, I do not quite understand the other two...

partial differential equations - difference between linear, semilinear and quasilinear PDE's - Mathematics Stack Exchange Stack Internal Knowledge at work Bring the best of human thought and AI automation together at your work. Explore Stack Internal difference between linear, semilinear and quasilinear PDE's Ask Question Asked 9 years, 6 months ago Modified 8 months ago Viewed 50k times 27 $\begingroup$ I know a PDE is linear when the dependent variable $u$ and its derivatives appear only to the first power. So, $u_t + u_x +5u = 1$ would be linear. However, I do not quite understand the other

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