Recent content by cheddacheeze

turns out computer didnt like the answer in equation form thanks

i differentiated yp twice plugged in yp'' yp' and yp into the differential and i got \frac{7}{3x^4}

yp = \frac{-7}{3x^2} tried plugging into the equation and didnt work, something must have gone wrong either in yp=uy1+vy2 or finding what v' was can anybody see what's wrong

have tried and checked and still have not got the right answer

Homework Statement You are given that two solutions to the homogeneous Euler-Cauchy equation x^2 \frac{d^2}{dx^2}y(x) - 5x \frac{d}{dx} y(x) + 5y(x) = 0 y1=x, y2=x^5 y''-\frac{5}{x}y'+\frac{5}{x^2}y=-\frac{49}{x^4} changing the equation to standard form use variation of parameters to find a...

turns out i just had to use rearranging to find my P(t)

\frac{1}{5} lnP - \frac{1}{5} ln(1000-P)= t+C lnP - ln(1000-P) = 5t+5c using log rules ln \frac{P}{1000-P} = 5t+5c multiplying by e \frac{P}{1000-P}=Ae^{5t} , A=e^{5c} P = (1000-P)(Ae^{5t}) multiplying it out P=1000Ae^{5t} - PAe^{5t} P + PAe^{5t} = 1000Ae^{5t} Ae^{5t}=...

does the equation become just for the subtitution \frac{-1}{ln(1000-P)}

i have totally forgot how to do integration using substitution, you mean du=-1dP will have to read up on it...

letting u = 1000-P du = -1? so confused

ok it seems the term \int \frac{1}{1000-P} is giving me trouble, what would be the substitution

cant i just do \frac{1}{5} \int \frac{1}{P} + \frac{1}{5} \int \frac{1}{1000-P} turning into: \frac{1}{5} lnP + \frac{1}{5} ln(1000-P) forgetting my basics...

ohhhhhh right i forgot i turned \frac{200}{P(1000-P)} into \frac{1}{5P}+\frac{1}{5000-5P} so its possible to do \frac{1}{5} \int \frac{1}{P} + \frac{1}{1000-P} ?

doesnt the 200 come from dP/dt=P(1000-P)/200 then i inversed dt/dP = 200/(P(1000-P)) and how do you make it so that it looks like a fraction? which tool was that

basically the equation becomes \int (1/5) (1/P + 1/1000-P) = \int 200dt or you can't take the common factor of 1/5? and how do you use parenthesis, still kind of new to these forums