First Order De

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The solution of dy/dx = y is

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$y = C e^{x}$

y = Cx

y = C/x

y = C

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Subject: mathematics
Chapter: differential equations
Topic: first order de
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

$y = C e^{x}$

Variable Separation: Group $y$ terms with $d y$ and $x$ terms with $d x$ .
- $\frac{d y}{y} = d x$
Integration:
- $\int \frac{1}{y} d y = \int d x$
- $ln ∣ y ∣ = x + K_{1}$ (where $K_{1}$ is constant)
Exponential Form: Raise $e$ to both sides.
- $∣ y ∣ = e^{x + K_{1}} = e^{K_{1}} e^{x}$
General Solution: Let $C = \pm e^{K_{1}}$ .
- $y = C e^{x}$ .

This medium difficulty mathematics question is from the chapter differential equations, covering the topic of first order de. It appeared in the 2025 exam.

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First Order De

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