Given that z = ax +sqrt (a^2 − 4y) + c is the complete integral of the PDE, p^2 − q^2 =4
determine its general integral.
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Expert's answer
2020-05-21T12:21:57-0400
Correction.
To understand the recall some theory.
Equation of the form f(p,q)=0 i.e. the equation contains p and q only.
Suppose that z(x,y)=ax+by+c is solution of equation, then
p=∂x∂z=aandq=∂y∂z=b
substitute the above in equation f(p,q)=0 , we get f(a,b)=0 on solving this we can get b=ϕ(a) , where ϕ is known function. Using b=ϕ(a) , the complete solution of the given partial equation is
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