Answer to Question #200427 in Differential Equations for Ayush

Question #200427

Equation 

x  y p  x  y q  z  z

2

cos( ) sin( )

is a quasi-linear equation


1
Expert's answer
2021-06-01T10:34:20-0400

Quasi-linear partial differential equations of first order can be written as


P(x,y,z)p+Q(x,y,z)q=R(x,y,z)(1)P(x,y,z)p+Q(x,y,z)q=R(x,y,z)\quad\quad (1)

where P,Q,RP,Q,R are functions of x,yx,y and zz . They do not involve pp or qq . Here, linear means that pp and qq appear to the first degree only.

In our case, the equation


cos(x+y)p+sin(x+y)q=z2\cos(x+y)p+\sin(x+y)q=z^2


is a quasi-linear equation.

 It's linear with respect to the derivatives (p and q)



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