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Exercise

dydx−3x=y\frac{dy}{dx}-3x=y

Step-by-step Solution

Learn how to solve trigonometric identities problems step by step online. Solve the differential equation dy/dx-3x=y. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -3x from both sides of the equation. Rearrange the differential equation. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=-1 and Q(x)=3x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
Solve the differential equation dy/dx-3x=y

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Final answer to the exercise

y=−3x−3+C0exy=-3x-3+C_0e^x

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dydx −3x=y
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