First Order De

Question

The solution of dy/dx = y is

RankGuru · Accepted Answer

1. **Variable Separation**: Group $y$ terms with $dy$ and $x$ terms with $dx$.
   - $\frac{dy}{y} = dx$
2. **Integration**:
   - $\int \frac{1}{y} dy = \int dx$
   - $\ln |y| = x + K_1$ (where $K_1$ is constant)
3. **Exponential Form**: Raise $e$ to both sides.
   - $|y| = e^{x + K_1} = e^{K_1} e^x$
4. **General Solution**: Let $C = \pm e^{K_1}$.
   - $y = C e^x$.

Rank Guru

First Order De

Select the correct option:

Solution

🔒 Solution Hidden from View

More first order de Practice Questions

The differential equation dy/dx = x/y represents

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