Math, asked by chauhanmuskan37, 9 months ago

p+q=sinx+siny solve this partial differential equation

Answers

Answered by Anonymous
16

order one is f (x,y,z,p,q)=0, where x,y are the independent variables, z is ... A solution of a partial differential equation of order one in ... so that, we have p = a + sin x and q = sin y – a …( 3)

Answered by AneesKakar
3

The complete integral of p+q=sinx+siny is z=ax-cosx-cosy-ay+C.

Given:

A differential equation p+q=sinx+siny.

To Find:

The solution of the differential equation.

Solution:

The complete integral is the solution of the partial differential equation.

Rewrite the given differential equation by shifting sinx to the left-hand side and q on the right-hand side of the equation.

p-sinx=siny-q

Let p-sinx=siny-q=a. Find dz=pdx+qdy.

dz=(a+sinx)dx+d(siny-a)dy\\

Integrate the above equation. The integration of sinx is -cosx and the integration of cosx is sinx.

z=ax-cosx-cosy-ay+C

The obtained equation cannot be integrated further hence it is the complete integral.

Thus, the complete integral of p+q=sinx+siny is z=ax-cosx-cosy-ay+C.

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