p+q=sinx+siny solve this partial differential equation
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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)
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The complete integral of is .
Given:
A differential equation .
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 to the left-hand side and on the right-hand side of the equation.
Let . Find .
Integrate the above equation. The integration of is and the integration of is .
The obtained equation cannot be integrated further hence it is the complete integral.
Thus, the complete integral of is .
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