Determine the general solution to the differential equation . |
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Identifier: The directions of the problem include the language “ general solution ” and “ differential equation ”. |
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Step 1: Identify your two variables. In this example the two variables are the y-variable and x-variable . |
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Step 2: Separate your equation by variables on to either side of the equals. 1) Multiply both sides of the equation by to get the y-variables on the same side as . 2) Multiply both sides of the equation by to get the x-variables on the same side as . |
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Step 3: Take the antiderivative of both sides of the equation. Both antiderivatives require you to run a u-substitution process. Keep in mind that you only need a single that works for the entire equation. |
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Step 4: Solve the equation you found in Step 3 to get the dependent variable ( y -variable) alone on one side of the equals. |
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Final Result: The general solution to the differential equation would be . |