The given differential equation is:

\[
y' = y
\]

This is a first-order linear differential equation, and we can solve it using separation of variables or by recognizing it as a standard equation with the solution \(y = Ce^x\), where \(C\) is a constant.

### Steps for solving:
1. **Rewrite the equation**:
   \[
   \frac{dy}{dx} = y
   \]

2. **Separate variables**:
   \[
   \frac{1}{y} \, dy = dx
   \]

3. **Integrate both sides**:
   \[
   \int \frac{1}{y} \, dy = \int dx
   \]
   The integral gives:
   \[
   \ln|y| = x + C_1
   \]
   where \(C_1\) is a constant of integration.

4. **Solve for \(y\)**:
   Exponentiate both sides to eliminate the logarithm:
   \[
   |y| = e^{x + C_1} = e^{x} \cdot e^{C_1}
   \]
   Let \(C = e^{C_1}\), so:
   \[
   y = Ce^x
   \]
   where \(C\) is a constant.

Thus, the general solution to the differential equation \(y' = y\) is:

\[
y = Ce^x
\]

Would you like more details or further clarification?

### Related Questions:
1. What is the solution to the equation \(y' = ky\), where \(k\) is a constant?
2. How do you solve the differential equation \(y' = y^2\)?
3. What is the role of the constant \(C\) in the solution of a differential equation?
4. How do you solve second-order differential equations like \(y'' = y\)?
5. Can you use Laplace transforms to solve differential equations like \(y' = y\)?

#### Tip:
When solving separable differential equations, always make sure to correctly apply the initial conditions to find the specific solution.

Discover the step-by-step solution to the differential equation y' = y using the separation of variables method. Learn how the solution leads to y = Ce^x, where C is a constant, and understand the key concepts of exponential functions and differential equations. Suitable for students in Grades 11-12 or early college.

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