Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Ordinary Differential Equations
Let f : ℝ → ℝ be a solution of the differential equation
\(\frac{d^2 y}{d x^2}-2 \frac{d y}{d x}+y=2 e^x \text { for } x \in \mathbb{R}\)
Consider the following statements.
P : If f(x) > 0 for all x ∈ ℝ, then f′(x) > 0 for all x ∈ ℝ.
Q : If f′(x) > 0 for all x ∈ ℝ, then f(x) > 0 for all x ∈ ℝ.
Then, which one of the following holds?
1
P is true but Q is false
2
P is false but Q is true
3
Both P and Q are true
4
Both P and Q are false