# Solve the Differential Equation (dy)/(dt)=(2y)/t

Separate the variables.
Multiply both sides by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite the equation.
Integrate both sides.
Set up an integral on each side.
The integral of with respect to is .
Integrate the right side.
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 .
Move all the terms containing a logarithm to the left side of the equation.
Simplify the left side.
Simplify .
Simplify each term.
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 .
Rewrite the equation as .
Multiply both sides by .
Simplify.
Simplify the left side.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Simplify the right side.
Reorder factors in .
Remove the absolute value term. This creates a on the right side of the equation because .
Group the constant terms together.
Simplify the constant of integration.
Combine constants with the plus or minus.
Solve the Differential Equation (dy)/(dt)=(2y)/t