Complex Variables and Partial Differential Equations (3130005)

Question-4c ( ii )

BE | Semester-3 Summer-2020 | 27-10-2020

Q4) (c ( ii ))

Find the complete integral of $p^{2} = qz$ .

p^{2} = qz

Taking,

q = pa - - - - - [1]

So,

p^{2} = paz \Rightarrow p = az & q = a^{2} z by [1] .

Solution:

dz = p dx + q dy

\Rightarrow dz = az dx + a^{2} z dy

\Rightarrow \frac{1}{z} dz = a dx + a^{2} dy \Rightarrow \int \frac{1}{z} dz = \int a dx + \int a^{2} dy

\Rightarrow \log z = ax + a^{2} y + b

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