Variable Separable
The solution of x dy - y dx = 0 is
Select the correct option:
Solution
y = Cx
- Rearrange Equation: xdy=ydx.
- Group Variables: Divide by xy (assuming x,y=0).
- ydy=xdx
- Integrate:
- lny=lnx+lnC
- lny=ln(Cx)
- Extract Variables: y=Cx.
- Note: This represents a family of straight lines passing through the origin.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More variable separable Practice Questions
A cup of coffee cools according to Newton's law so that \frac{dT}{dt} = -k(T - T_s); identify the co...
A cup of coffee cools according to Newton's law so that \frac{dT}{dt} = -k(T - T_s); identify the co...
A population grows so that its rate of change is proportional to its current size, modeled by \frac{...
A population grows so that its rate of change is proportional to its current size, modeled by \frac{...
Solve the differential equation \frac{dy}{dx} = e^{x-y} and express the general solution relating th...
Solve the differential equation \frac{dy}{dx} = e^{x-y} and express the general solution relating th...
Solve the separable differential equation \frac{dy}{dx} = \frac{1+y^2}{1+x^2} subject to the initial...
Solve the separable differential equation \frac{dy}{dx} = \frac{1+y^2}{1+x^2} subject to the initial...
About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- variable separable
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
y = Cx
- Rearrange Equation: xdy=ydx.
- Group Variables: Divide by xy (assuming x,y=0).
- ydy=xdx
- Integrate:
- lny=lnx+lnC
- lny=ln(Cx)
- Extract Variables: y=Cx.
- Note: This represents a family of straight lines passing through the origin.
This medium difficulty mathematics question is from the chapter differential equations, covering the topic of variable separable. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse differential equations questions on RankGuru.