Question

Solve the following : p + q = cos x + cos y.​

Answer 1

Answer:

U=(x-y) - cosx + Sony + c.

Step-by-step explanation:

Rewrite the equation as U_x + U_y = sinx + cosy where U(x,y) is the

unknown function. The structure of the equation suggest the

assumption : Ux,y) = F(x) + G(y) .Then the equation becomes

F’(x) + G’(y) = sinx + cosy . Follows

( F’(x) - sinx ) + ( G’(y) - cosy ) =0 , and

( F’(x) - sinx ) = - ( G’(y) - cosy ) = K. Integrating both equation gives

F(x) = Kx - cosx + C1

G(y) = -Ky + siny + C2 , then the solution should be

U = K( x - y) - cosx + siny + C .