First Order De
Easymathematics
The differential equation dy/dx = x/y represents
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Solution
Incorrect! Answer:
Variable separable
- Test for Separation: Can we write g(y)dy=f(x)dx?
- dxdyā=yxāā¹ydy=xdx.
- Conclusion: Since the variables x and y can be completely separated to opposite sides of the equality, the equation is Variable Separable.
- Solution (ext.): Integrating ydy=xdx gives 2y2ā=2x2ā+C, which represents a family of hyperbolas (y2āx2=K).
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More first order de Practice Questions
EasyJEE_MAIN
The degree of the differential equation (dy/dx)Ā³ + 2(dy/dx)Ā² + y = 0 is
The degree of the differential equation (dy/dx)Ā³ + 2(dy/dx)Ā² + y = 0 is
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MediumJEE_MAIN
The solution of dy/dx = y is
The solution of dy/dx = y is
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The order of the differential equation dĀ²y/dxĀ² + 3(dy/dx) + 2y = 0 is
The order of the differential equation dĀ²y/dxĀ² + 3(dy/dx) + 2y = 0 is
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MediumJEE_ADVANCED
The solution of dy/dx + y = 0 with initial condition y(0) = 1 is
The solution of dy/dx + y = 0 with initial condition y(0) = 1 is
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About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- first order de
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
Variable separable
- Test for Separation: Can we write g(y)dy=f(x)dx?
- dxdyā=yxāā¹ydy=xdx.
- Conclusion: Since the variables x and y can be completely separated to opposite sides of the equality, the equation is Variable Separable.
- Solution (ext.): Integrating ydy=xdx gives 2y2ā=2x2ā+C, which represents a family of hyperbolas (y2āx2=K).
This easy 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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