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- Exact Differential Equation
- Linear Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Rewrite the differential equation using Leibniz notation
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}-2y=x^2e^{2x}$
Learn how to solve differential equations problems step by step online. Solve the differential equation y^'-2y=x^2e^(2x). Rewrite the differential equation using Leibniz notation. 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)=-2 and Q(x)=x^2e^{2x}. 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. So the integrating factor \mu(x) is.
