QuestionGiven the differential equation , find the particular solution, , with the initial condition .
Answer Attempt 1 out of 2
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Studdy Solution
STEP 1
1. The differential equation is separable.
2. We can integrate both sides to find the particular solution.
3. The initial condition will be used to find the constant of integration.
STEP 2
1. Separate the variables.
2. Integrate both sides.
3. Solve for the constant of integration using the initial condition.
4. Write the particular solution.
STEP 3
Separate the variables by multiplying both sides by and :
STEP 4
Integrate both sides:
The left side becomes:
The right side becomes:
Combine the constants of integration:
STEP 5
Use the initial condition to find :
Substitute and into the equation:
STEP 6
Substitute back into the equation:
Solve for :
Since , we choose the negative root:
The particular solution is:
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