Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Partial Differential Equations Lagrange and Charpit Methods
Consider the Cauchy problem
\(\rm x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}=u;\)
𝑢 = 𝑓(𝑡) on the initial curve Γ = (𝑡, 𝑡); 𝑡 > 0.
Consider the following statements:
𝑃: If 𝑓(𝑡) = 2𝑡 + 1, then there exists a unique solution to the Cauchy problem in a neighbourhood of Γ.
𝑄: If 𝑓(𝑡) = 2𝑡 − 1, then there exist infinitely many solutions to the Cauchy problem in a neighbourhood of Γ.
Then
1
both 𝑃 and 𝑄 are TRUE
2
𝑃 is FALSE and 𝑄 is TRUE
3
𝑃 is TRUE and 𝑄 is FALSE
4
both 𝑃 and 𝑄 are FALSE
5
Question Not Attempted