Calculus Examples

Verify the Differential Equation Solution
Step 1
Find .
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Step 1.1
Differentiate both sides of the equation.
Step 1.2
The derivative of with respect to is .
Step 1.3
Differentiate using the Power Rule which states that is where .
Step 1.4
Reform the equation by setting the left side equal to the right side.
Step 2
Substitute into the given differential equation.
Step 3
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Cancel the common factors.
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Step 3.2.1
Raise to the power of .
Step 3.2.2
Factor out of .
Step 3.2.3
Cancel the common factor.
Step 3.2.4
Rewrite the expression.
Step 3.2.5
Divide by .
Step 4
The given solution satisfies the given differential equation.
is a solution to
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