Hey guys,
I am a bit stuck answering this question. The question being:
If dy/dx = (x+3)(x-2), Find y
I expanded the brackets first of all but a bit stuck from here. Can anyone give me some guidance on what to do next?
Thanks
Danthemaths
Hey guys,
I am a bit stuck answering this question. The question being:
If dy/dx = (x+3)(x-2), Find y
I expanded the brackets first of all but a bit stuck from here. Can anyone give me some guidance on what to do next?
Thanks
Danthemaths
do we get two answers? because x=-3 and another x=2
thats the part i was stuck on, it there two answers to this question??
coz once the brackets are expanded you get dy/dx=x^2-x-1
integrate that you get: y=x^3/3-1
then dont you sub each x in? so y= (-3)^3/3-1 and then sub the other in to get y=(2)^3/3-1
and you get 2 y answers?
is this how you do this?
I'm assuming you want to determine f(x), a.k.a solving a differential equation. Note that the equation is separable: Pauls Online Notes : Differential Equations - Separable Equations
Basically you need to get the differentials to be on separate side of the equality. Therefore dy = (x-2)(x+3)dx. Integrate both sides to get a general expression for f(x). I believe 'y" is referring to the solution of the differential equation in this question.
Are you not taking a Calculus course? That surely looks like a Calculus question.
If $\displaystyle \frac{dy}{dx}= (x+3)(x-2)$, then $\displaystyle y= \int (x+3)(x- 2)dx$. Once you have multiplied (x+3)(x-2) that will be an easy integral.
(There are not two solutions. There are, strictly speaking, an infinite number of solutions, one for each choice of the "constant of integration". But the fact that there two factors is not relevant.)