Complex Variables and Partial Differential Equations (3130005)

Question-4a

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

Q4) (a)

Solve $xp + yq = x - y$

Auxiliary equation:

\frac{dx}{P} = \frac{dy}{Q} = \frac{dz}{R} \Rightarrow \frac{dx}{x} = \frac{dy}{y} = \frac{dz}{x - y}

Group-I $\frac{dx}{x} = \frac{dy}{y}$

\int \frac{dx}{x} = \int \frac{dy}{y} \Rightarrow \log x = \log y + \log c_{1} \Rightarrow \frac{x}{y} = c_{1}

Group-II $\frac{dx - dy}{x - y} = \frac{dz}{x - y}$

\Rightarrow dx - dy = dz

\Rightarrow \int 1 dx - \int 1 dy = \int 1 dz

\Rightarrow x - y = z + c_{2} \Rightarrow x - y - z = c_{2}

Solution:

f (\frac{x}{y}, x - y - z) = 0

Questions

Go to Question Paper