https://file.aiquickdraw.com/mathbot/file/1726238416154haxrkam6.jpg

The equation given in the image is:

\[
\frac{dy}{dx} - 9 = 0
\]

To solve for \( y \), we first rearrange the equation:

\[
\frac{dy}{dx} = 9
\]

Now, integrate both sides with respect to \( x \):

\[
y = \int 9 \, dx
\]

This gives:

\[
y = 9x + C
\]

where \( C \) is the constant of integration.

Thus, the solution is:

\[
y = 9x + C
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you determine the constant \( C \) in differential equations?
2. Can you solve similar differential equations with variable coefficients?
3. What is the general approach to solving first-order linear differential equations?
4. How can initial conditions affect the value of \( C \)?
5. What is the physical meaning of such differential equations in real-world contexts?

### Tip:
When solving differential equations, always check if any initial or boundary conditions are given to determine the constant of integration.

Learn how to solve the first-order differential equation dy/dx - 9 = 0 with a detailed step-by-step solution. This problem covers key calculus concepts such as integration and the constant of integration. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation