1st order ODE -partial fractions

[ijd5000]

Hi,
i'm having trouble with the partial fraction decomposition for the ODE:

v'=1250-2v^2

rearranged to:

(1/(1250-2v^2))v'=1

integrating both sides I came to a need for partial fractions.

A/(25sqrt(2)+sqrt(2)v) + B/(25sqrt(2)-sqrt(2)v)

by equating coefficients i came up with A=3/100sqrt(2) and B=1/100sqrt(2).

I was told this is not right.

 

[Deleted member 4993]

Hi,
i'm having trouble with the partial fraction decomposition for the ODE:

v'=1250-2v^2

rearranged to:

(1/(1250-2v^2))v'=1

integrating both sides I came to a need for partial fractions.

A/(25sqrt(2)+sqrt(2)v) + B/(25sqrt(2)-sqrt(2)v)

by equating coefficients i came up with A=3/100sqrt(2) and B=1/100sqrt(2).

I was told this is not right.

\(\displaystyle \dfrac{dv}{625-v^2} \ = \ 2dx\)

\(\displaystyle \dfrac{dv}{25^2-v^2} \ = \ 2dx\)

\(\displaystyle \dfrac{dv}{25-v} \ + \ \dfrac{dv}{25+v} \ = \ 100dx\)

\(\displaystyle ln\left (\dfrac{25+v}{25-v}\right ) \ = \ 100x + C\) .....edited

 

[ijd5000]

thanks