Calculus Examples

Solve the Differential Equation (dy)/(dx)=(x^2-1)/(y^2+1)
Step 1
Separate the variables.
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Step 1.1
Multiply both sides by .
Step 1.2
Simplify.
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Step 1.2.1
Simplify the numerator.
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Step 1.2.1.1
Rewrite as .
Step 1.2.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.2.2
Cancel the common factor of .
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Step 1.2.2.1
Cancel the common factor.
Step 1.2.2.2
Rewrite the expression.
Step 1.2.3
Expand using the FOIL Method.
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Step 1.2.3.1
Apply the distributive property.
Step 1.2.3.2
Apply the distributive property.
Step 1.2.3.3
Apply the distributive property.
Step 1.2.4
Simplify and combine like terms.
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Step 1.2.4.1
Simplify each term.
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Step 1.2.4.1.1
Multiply by .
Step 1.2.4.1.2
Move to the left of .
Step 1.2.4.1.3
Rewrite as .
Step 1.2.4.1.4
Multiply by .
Step 1.2.4.1.5
Multiply by .
Step 1.2.4.2
Add and .
Step 1.2.4.3
Add and .
Step 1.3
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
Integrate the left side.
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Step 2.2.1
Split the single integral into multiple integrals.
Step 2.2.2
By the Power Rule, the integral of with respect to is .
Step 2.2.3
Apply the constant rule.
Step 2.2.4
Simplify.
Step 2.3
Integrate the right side.
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Step 2.3.1
Split the single integral into multiple integrals.
Step 2.3.2
By the Power Rule, the integral of with respect to is .
Step 2.3.3
Apply the constant rule.
Step 2.3.4
Simplify.
Step 2.4
Group the constant of integration on the right side as .