how do you check if the general solution obtained in a differential equation is correct?

Question

anonymous · Answer

Plug and Play

anonymous · Answer

You should be able to take the derivative as many times as you need to in order to get the original diff eq

unklerhaukus · Answer

Differentiate the solution
you should get back the differential equation

lgbasallote · Answer

really? that means the DE is just integration??

anonymous · Answer

That's a way of thinking about it, except that the differential equation is an equation that relates a variable to its derivative.  It's kind of the same, but the statement isn't 100% accurate.

lgbasallote · Answer

why not?

unklerhaukus · Answer

attachment

lgbasallote · Answer

WAHHHH pdfs =_=

lgbasallote · Answer

well anyway i got what i was asking so thanks lol =))

unklerhaukus · Answer

you can't open it?

unklerhaukus · Answer

For this Differential equation$$\frac{\text d y}{\text d x}+\frac{x+y}{x}=0$$
I solved and got$$x^2+2xy = k^2 $$

Differentiating
$$\frac{\text d }{ \text dx}\left(x^2+2xy \right)=\frac{\text d }{ \text dx}\left(k^2\right)$$
Returns the original equation
$$\frac{\text d y}{\text d x}+\frac{x+y}{x}=0$$