Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Partial Differential Equations Lagrange and Charpit Methods
The general solution of the equation
\(x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=0\) is
1
\(z=\varphi\left(\frac{|x|}{|y|}\right)\), φ ∈ C1 (ℝ)
2
\(z=\varphi\left(\frac{x-1}{y}\right)\), φ ∈ C1 (ℝ)
3
\(z=\varphi\left(\frac{x+1}{y}\right)\), φ ∈ C1 (ℝ)
4
z = φ(|x| + |y|), φ ∈ C1 (ℝ)