Find $\displaystyle y$ as a function of $\displaystyle x$ if
$\displaystyle \frac{dy}{dx} = y(2x+1)$
and $\displaystyle y = -3$ when $\displaystyle x = 0$.
Any idea on where to get started? I have no clue...
Find $\displaystyle y$ as a function of $\displaystyle x$ if
$\displaystyle \frac{dy}{dx} = y(2x+1)$
and $\displaystyle y = -3$ when $\displaystyle x = 0$.
Any idea on where to get started? I have no clue...
$\displaystyle y=-3$ when $\displaystyle x=0$ will give you the value of the constant $\displaystyle C$ that is in your function. Integrate first to find an equation of y as a function of x. then plug in the given values of y and x, which will give you the value of the constant.
The Cs are arbitrary constants, and when you do the integral of both the left/right side it is sufficient to have only one constant variable (i.e. only one C) either on the left side or right side of your equation.
To obtain y, put everything up to the e. This will bring down y due to the rule of logs and that is your answer (assuming you've done the rest correct)
NO. Thats a bit too impulsive.
The value of constant is not same on both the sides. if you have written C on the left side, then express the constant on the right hand side with another letter. (say $\displaystyle C'$). After that, bring all the constants on the same side. this gives you
$\displaystyle ln |y| = x^2 + x + (C'-C)$
note that $\displaystyle C'-C$, the difference of two constants, is also a constant. For convenience, denote it with another letter.
then find y