## anonymous one year ago Solve the equation for y in terms of x: 3y + 2y^2 = -e^(-x) - e^(x) + 7

1. dinamix

its not differential equation ?

2. anonymous

Ill post the entire question and maybe that'll help

3. anonymous

Find the solution to the initial value problem in explicit form $y' = \frac{e^{-x} - e^{x}}{3 + 4y}$

4. anonymous

y(0) = 1

5. anonymous

@dan815 ?

6. freckles

y'*y doesn't equal y^2

7. freckles

$(3+4y) dy=(e^{-x}-e^{x} )dx$ equation is seperable integrate both sides

8. freckles

oh wait are you saying you think you found the solution to that?

9. anonymous

yes i believe so and now i need it in explicit form

10. anonymous

I believe i have found the correct value for the constant c given the initial value as well

11. freckles

your solution is correct

12. freckles

don't believe you can find explicit form

13. anonymous

the answer in the back of the book has done it some how.

14. freckles

hmmm well you have a quadratic in terms of y

15. freckles

$2y^2-3y+e^{-x}+e^{x}-7=0 \\ y=\frac{-(-3) \pm \sqrt{(-3)^2-4(2)(e^{-x}+e^{x}-7)}}{2(2)}$

16. freckles

though the implicit form looks much better to me

17. anonymous

that looks like the answer, how'd you do that?!

18. freckles

it is a quadratic in terms of y

19. freckles

all i did was use the quadratic formula

20. freckles

a=2 b=-3 c=e^(-x)+e^x-7

21. anonymous

ohhhhh

22. anonymous

i gotcha now

23. anonymous

Thank you!!!!!!

24. freckles

np