hi, im having problems with these...
find the general solutions for:
t^2 dx/dt = x +1
and
y^1/2 dy/dx = y/x
if someone could go step by step on those i would be very happy!
please help!
many thanks
Theser are SDEs(seperable differential equations)...for example the first one $\displaystyle t^2\frac{dx}{dt}=x+1$...sepearing we get $\displaystyle \frac{1}{x+1}dx=\frac{dt}{t^2}$...integrating both sides we get $\displaystyle ln|x+1|=\frac{-1}{t}+C$ now solving for the function x which is what we want we get $\displaystyle x=Ce^{\frac{-1}{t}}-1$ where C is a constant..
You want to get the dx's with the x's and the dt's with the dt.....and then integrate as you normally would then solve for teh function they ask you to(the function you are supposed to solve for is the whatever letter is on the top of the fraction...example $\displaystyle \frac{dy}{dx}$ it would be solve for y)
Oh right, thanks
and for the 2nd one i get..
y^-2 dy/dx = y/x
integrate y^1/2 /y dy = integrate 1/x dx
integrate y^-1/2 dy = integrate x^-1 dx
= 1/2 y^1/2 = x
?
i get confused with the last bit, you add 1 to the power and divide by the new power dont you?
thanks a lot so far!