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-- yet another maths problem

yet another maths problem

ok anyone happen to know how to find the genral solution to a ordinary differential equations (ODE's)


like how would i go about finding the genral solution of the ODE

ds/dt = s + 1


what is the methods i would follow to solve problems of a similar nature?

We need a Homework forum. And a forum where you can post essays for others to use.

You need an intigrating factor

ds/dt - s = 1

IF = -1

which is exp(int(-1,t))=exp(-t)

then multiply that to the whole equation


so

ds/dt*exp(-t) - s*exp(-t) = exp(-t)


now the left hand side is a derivative:

d(s*exp(-t))/dt= exp(-t)

so you intigrate both sides and then divide by the exp(-t)

which gives you:

s*exp(-t) = -exp(-t)+C

so s= -1+C/exp(-t)= -1+C*exp(t)

quote:

Originally posted by Neo nEro You need an intigrating factor ds/dt - s = 1 IF = -1 which is exp(int(-1,t))=exp(-t)

how do you find a sutable integrating factor?

its not really the answer to the question im after as much as how to answer these questions.

quote:

Originally posted by dukes how do you find a sutable integrating factor? its not really the answer to the question im after as much as how to answer these questions.

if its a first order liner equation then the integrating factor is the junk in front of the s term once the equation is in standard form

i think im gonna give up because im never gonna learn this in time to hand in my coursework.

i may beable to grasp how to do that question (i still am a little confused with it but the next one is a tad more complicated. as in i cant get it in the form

ds/dt + s = ??

and such.

arg should have been to uni more

quote:

Originally posted by dukes i think im gonna give up because im never gonna learn this in time to hand in my coursework. i may beable to grasp how to do that question (i still am a little confused with it but the next one is a tad more complicated. as in i cant get it in the form ds/dt + s = ?? and such. arg should have been to uni more

you want it in the form 1*s' + f(t)*s = g(t)

e^int(f(t)) is your integrating factor

all this is in your book some place

laplace transform it...its by far the easiest way...and if u dont know what that is just look up the rules for it in some book...it will make ur life a billion times easier

Separation of variables is the simplest way to solve this problem. Laplace transform would also be very easy, but just slightly more complex.

quote:

Originally posted by Neo nEro You need an intigrating factor ds/dt - s = 1 IF = -1 which is exp(int(-1,t))=exp(-t) then multiply that to the whole equation so ds/dt*exp(-t) - s*exp(-t) = exp(-t) now the left hand side is a derivative: d(s*exp(-t))/dt= exp(-t) so you intigrate both sides and then divide by the exp(-t) which gives you: s*exp(-t) = -exp(-t)+C so s= -1+C/exp(-t)= -1+C*exp(t)

how do you use this in real life :S, always found that a more intresting question than the equation it self @ school.

quote:

Originally posted by Noctone Separation of variables is the simplest way to solve this problem. Laplace transform would also be very easy, but just slightly more complex.

can't seperate variables

quote:

Originally posted by Massive84 how do you use this in real life :S, always found that a more intresting question than the equation it self @ school.

well this equation could describe the motion of a car in response to pushing the gas or maybe the current through a circuit. making it possible for you to have the freedom of a car and listen to music respectively

quote:

can't seperate variables

I beg to differ.


ds/dt=s+1

ds(1/(s+1))=dt
ln(s+1)=t+C
e^(ln(s+1))=e^(t+C)
e^(t+C)=e^t*e^C=Ae^t
s+1=Ae^t
s=(Ae^t)-1

Tell me again why I can't separate variables?

generally you can't,

the other method can solve any general first order linear equation.

quote:

Originally posted by caddyshack well this equation could describe the motion of a car in response to pushing the gas or maybe the current through a circuit. making it possible for you to have the freedom of a car and listen to music respectively

lol owned.

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