Calculus Examples

Solve the Differential Equation
Step 1
Rewrite the equation.
Step 2
Integrate both sides.
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Step 2.1
Set up an integral on each side.
Step 2.2
Apply the constant rule.
Step 2.3
Integrate the right side.
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Step 2.3.1
Let . Then . Rewrite using and .
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Step 2.3.1.1
Let . Find .
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Step 2.3.1.1.1
Differentiate .
Step 2.3.1.1.2
By the Sum Rule, the derivative of with respect to is .
Step 2.3.1.1.3
Differentiate using the Power Rule which states that is where .
Step 2.3.1.1.4
Since is constant with respect to , the derivative of with respect to is .
Step 2.3.1.1.5
Add and .
Step 2.3.1.2
Rewrite the problem using and .
Step 2.3.2
By the Power Rule, the integral of with respect to is .
Step 2.3.3
Replace all occurrences of with .
Step 2.4
Group the constant of integration on the right side as .
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