Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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![**Initial Value Problem Solving**
To solve the initial-value problem for \( x \) as a function of \( t \), follow the steps below:
Given Equation:
\[ \left(2t^3 - 2t^2 + t - 1\right) \frac{dx}{dt} = 3 \]
With the initial condition:
\[ x(2) = 0 \]
1. **Separate Variables:**
Rearrange the given equation to separate variables \( t \) and \( x \).
2. **Integrate:**
Integrate both sides with respect to \( t \).
3. **Solve for \( x(t) \):**
Use the given initial condition to find the particular solution to the differential equation.
By following these steps, we can find \( x \) as a function of \( t \).](https://content.bartleby.com/qna-images/question/b504023a-9c44-4030-9585-d80b6f747933/469d6b41-8b5c-4b00-873f-e4322c92b040/n1zpfk9.png)
Transcribed Image Text:**Initial Value Problem Solving**
To solve the initial-value problem for \( x \) as a function of \( t \), follow the steps below:
Given Equation:
\[ \left(2t^3 - 2t^2 + t - 1\right) \frac{dx}{dt} = 3 \]
With the initial condition:
\[ x(2) = 0 \]
1. **Separate Variables:**
Rearrange the given equation to separate variables \( t \) and \( x \).
2. **Integrate:**
Integrate both sides with respect to \( t \).
3. **Solve for \( x(t) \):**
Use the given initial condition to find the particular solution to the differential equation.
By following these steps, we can find \( x \) as a function of \( t \).
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