Final answer to the problem
$y=\left(\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+\frac{1}{e^{\frac{1}{2}x^2}}+C_0\right)e^{\frac{1}{2}x^2}$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Scegliere un'opzione
- Equazione differenziale esatta
- Equazione differenziale lineare
- Equazione differenziale separabile
- Equazione differenziale omogenea
- Prodotto di binomi con termine comune
- Metodo FOIL
- Load more...
Can't find a method? Tell us so we can add it.
1
Rewrite the differential equation using Leibniz notation
$\frac{dy}{dx}-xy=1-x$
Learn how to solve problems step by step online.
$\frac{dy}{dx}-xy=1-x$
Learn how to solve problems step by step online. y^'-xy=1-x. 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)=-x and Q(x)=1-x. 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
$y=\left(\sum_{n=0}^{\infty } \frac{{\left(\left(-\frac{1}{2}\right)\right)}^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+\frac{1}{e^{\frac{1}{2}x^2}}+C_0\right)e^{\frac{1}{2}x^2}$
