Solve the Differential Equation x(dy)/(dx)=2y

Math
Separate the variables.
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Divide each term in by and simplify.
Multiply both sides by .
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite the equation.
Integrate both sides.
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Set up an integral on each side.
The integral of with respect to is .
Integrate the right side.
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Since is constant with respect to , move out of the integral.
The integral of with respect to is .
Simplify.
Group the constant of integration on the right side as .
Solve for .
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Move all the terms containing a logarithm to the left side of the equation.
Simplify the left side.
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Simplify .
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Simplify each term.
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Simplify by moving inside the logarithm.
Remove the absolute value in because exponentiations with even powers are always positive.
Use the quotient property of logarithms, .
To solve for , rewrite the equation using properties of logarithms.
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for .
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Rewrite the equation as .
Multiply both sides by .
Simplify.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify the right side.
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Reorder factors in .
Remove the absolute value term. This creates a on the right side of the equation because .
Group the constant terms together.
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Simplify the constant of integration.
Combine constants with the plus or minus.
Solve the Differential Equation x(dy)/(dx)=2y

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