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Find the general solution of dy/dx = 3x^2. (2020)
Practice Questions
Q1
Find the general solution of dy/dx = 3x^2. (2020)
y = x^3 + C
y = 3x^3 + C
y = x^2 + C
y = 3x + C
Questions & Step-by-Step Solutions
Find the general solution of dy/dx = 3x^2. (2020)
Steps
Concepts
Step 1: Start with the equation dy/dx = 3x^2.
Step 2: Recognize that dy/dx means we need to find the function y by integrating the right side.
Step 3: Integrate 3x^2 with respect to x. This means we find the antiderivative.
Step 4: The integral of 3x^2 is x^3 + C, where C is the constant of integration.
Step 5: Write the general solution as y = x^3 + C.
Differential Equations
– The question tests the ability to solve a first-order ordinary differential equation using integration.
Integration
– The solution requires knowledge of basic integration techniques to find the antiderivative of a polynomial function.
General Solution
– Understanding the concept of a general solution, which includes an arbitrary constant (C) representing the family of solutions.
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