Find the solution y(x) for the 1st-order linear IVP. y' + 2y = 20 ; y(0) = 1 Hint: You may verify that one particular solution is yp = 10. Then, you could next focus on finding yc .. Or, if you prefer, you can ignore that hint and find the general solution by some other method.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Solving a 1st-Order Linear Initial Value Problem (IVP)

**Problem:**

Find the solution \( y(x) \) for the 1st-order linear IVP.

\[ y' + 2y = 20 \; ; \; y(0) = 1 \]

**Hint:**

You may verify that one particular solution is \( y_p = 10 \). Then, you could next focus on finding \( y_c \)…

Or, if you prefer, you can ignore that hint and find the general solution by some other method. 

---

For an educational purpose:

- You may start by verifying the particular solution.
- Use methods such as integrating factor or homogeneous and particular solutions to solve the given differential equation.
Transcribed Image Text:### Solving a 1st-Order Linear Initial Value Problem (IVP) **Problem:** Find the solution \( y(x) \) for the 1st-order linear IVP. \[ y' + 2y = 20 \; ; \; y(0) = 1 \] **Hint:** You may verify that one particular solution is \( y_p = 10 \). Then, you could next focus on finding \( y_c \)… Or, if you prefer, you can ignore that hint and find the general solution by some other method. --- For an educational purpose: - You may start by verifying the particular solution. - Use methods such as integrating factor or homogeneous and particular solutions to solve the given differential equation.
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