Question

hello guys, can someone give me an explanation and a couple of exercises on how to solve some basic differential equations?
Thank you beforehand

Answer 1

https://www.khanacademy.org/math/differential-equations/first-order-differential-equations/differential-equations-intro/v/what-is-a-differential-equation

Answer 2

thank you

Answer 3

Did you get what you were finding ?

Answer 4

http://tutorial.math.lamar.edu/Classes/DE/IntroFirstOrder.aspx

Answer 5

yup, thank you very much

Answer 6

All right! your welcome =')

Answer 7

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx
Those are dry, but can be helpful! :)

Answer 8

Solve the differential equation for \(y(x)\), given the initial condition \(y_0=y(0)\)\[\frac{\mathrm dy}{\mathrm dx}=x,\qquad\qquad y_0=1\]__________________________________

Separate the variables, and integrate
\[\begin{align}\mathrm dy& =x\,\mathrm dx\\\int\mathrm dy&=\int x\mathrm dx\\y&=x^2/2+c\end{align}\]
Applying the initial condition, we find the constant of integration
\[\qquad y(0)=c=1\]
The solution is :
\[y(x)=x^2/2+1\]

Differentiating the solution gives back the original DE as expected.
\[\frac{\mathrm dy}{\mathrm dx}=x\]