First Order De

Question

The differential equation dy/dx = x/y represents

RankGuru · Accepted Answer

1. **Test for Separation**: Can we write $g(y)dy = f(x)dx$?
   - $\frac{dy}{dx} = \frac{x}{y} \implies y \, dy = x \, dx$.
2. **Conclusion**: Since the variables $x$ and $y$ can be completely separated to opposite sides of the equality, the equation is **Variable Separable**.
3. **Solution** (ext.): Integrating $y \, dy = x \, dx$ gives $\frac{y^2}{2} = \frac{x^2}{2} + C$, which represents a family of hyperbolas ($y^2 - x^2 = K$).

Rank Guru

First Order De

Select the correct option:

Solution

🔒 Solution Hidden from View

More first order de Practice Questions

The degree of the differential equation (dy/dx)³ + 2(dy/dx)² + y = 0 is

The solution of dy/dx = y is

The order of the differential equation d²y/dx² + 3(dy/dx) + 2y = 0 is

The solution of dy/dx + y = 0 with initial condition y(0) = 1 is

About This Question