Final answer to the problem
$y=\left(\frac{x^{3}}{3}+C_0\right)e^{2x}$
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Step-by-step Solution
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- Equazione differenziale esatta
- Equazione differenziale lineare
- Equazione differenziale separabile
- Equazione differenziale omogenea
- Prodotto di binomi con termine comune
- Metodo FOIL
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1
Rewrite the differential equation using Leibniz notation
$\frac{dy}{dx}-2y=x^2e^{2x}$
Learn how to solve equazioni differenziali problems step by step online.
$\frac{dy}{dx}-2y=x^2e^{2x}$
Learn how to solve equazioni differenziali problems step by step online. 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.
Final answer to the problem
$y=\left(\frac{x^{3}}{3}+C_0\right)e^{2x}$
