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Solve the differential equation dy/dx = 3x^2.
Solve the differential equation dy/dx = 3x^2.
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Practice Questions
1 question
Q1
Solve the differential equation dy/dx = 3x^2.
y = x^3 + C
y = 3x^3 + C
y = x^2 + C
y = 3x + C
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Integrating both sides gives y = x^3 + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Solve the differential equation dy/dx = 3x^2.
Solution:
Integrating both sides gives y = x^3 + C.
Steps: 5
Show Steps
Step 1: Start with the given differential equation: dy/dx = 3x^2.
Step 2: To solve for y, we need to integrate both sides of the equation with respect to x.
Step 3: Integrate the right side: ∫3x^2 dx. This gives us x^3 + C, where C is the constant of integration.
Step 4: The left side, ∫dy, simply gives us y.
Step 5: Combine the results from the integration: y = x^3 + C.
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