Differential Equations
Let f(x) be differentiable s.t. f′(x)=2−f(x)/x and f(1)=1. Then f(x) is:
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About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- differential equations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
x
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Rearrange to standard Linear DE form: f′(x)+x1f(x)=2. P(x)=1/x,Q(x)=2.
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Integrating Factor: IF =e∫1/xdx=x.
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Solve: xf(x)=∫2xdx+C xf(x)=x2+C f(x)=x+C/x.
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Apply condition f(1)=1: 1=1+C/1⟹C=0. So, f(x)=x.
This easy difficulty mathematics question is from the chapter differential equations, covering the topic of differential equations. It appeared in the 2025 exam.
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