Answer to Question #120928 in Differential Equations for Kallan Roy

Question

z = f(x + ay) + g(x − ay)

Answer 1

We can form the PDE by eliminating f and g from

z=f(x+ay)+g(x-ay) ....(1)

Differentiate (1) w.r.t. x and y ,we get

p=f^'(x+ay)+g^'(x-ay) .....(2)

q=f^'(x+ay).a+g^'(x-ay).(-a) ...(3)

Now differentiate (2) &(3) w. r. t to x and y respectively

r=f^"(x+ay)+g^"(x-ay)

t=f^"(x+ay).a²+g^"(x-ay)(-a)²

Now t= a²[ f^"(x+ay)+g^"(x-ay)]

Hence , t=a².r

This is the required PDE

Ans . : t=a².r