Given the following differential equation find the solution that passes through (1,1). You may use separation of variables.

dy/dt = t / (y^2 * sqrt(1+t^2))

Question

Given the following differential equation find the solution that passes through (1,1). You may use separation of variables.

dy/dt = t / (y^2 * sqrt(1+t^2))

amistre64 · Answer

[S] y^2 dy =[S] t/sqrt(1+t^2) dt

amistre64 · Answer

(1/3)y^3 = (1/2)(sqrt(1+t^2))  is that right :)

amistre64 · Answer

i think that ''1/2'' cancels ....

amistre64 · Answer

(1/3)y^3 = sqrt(1+t^2) +c

1,1 seems like coordinantes, but are they t=1 and y=1?

amistre64 · Answer

(1/3) = sqrt(2) +c

c = sqrt(2)/3

(1/3) y^3 = sqrt(1+t^2) + sqrt(2)/3....thats the best i got....

anonymous · Answer

Thank you very much!

c = (1/3) - sqrt(2)

The final answer is:
(3(sqrt(1+t^2)+((1/3)-sqrt(2))))^(1/3) = y(t)

Thanks!

amistre64 · Answer

youre welcome :)  just glad I was right  lol

amistre64 · Answer

er...kinda right