Solve the equation for y in terms of x:

3y + 2y^2 = -e^(-x) - e^(x) + 7

Question

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

dinamix · Answer

its not differential equation ?

anonymous · Answer

Ill post the entire question and maybe that'll help

anonymous · Answer

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

anonymous · Answer

y(0) = 1

anonymous · Answer

@dan815 ?

freckles · Answer

y'*y doesn't equal y^2

freckles · Answer

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

freckles · Answer

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

anonymous · Answer

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

anonymous · Answer

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

freckles · Answer

your solution is correct

freckles · Answer

don't believe you can find explicit form

anonymous · Answer

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

freckles · Answer

hmmm
well you have a quadratic in terms of y

freckles · Answer

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

freckles · Answer

though the implicit form looks much better to me

anonymous · Answer

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

freckles · Answer

it is a quadratic in terms of y

freckles · Answer

all i did was use the quadratic formula

freckles · Answer

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

anonymous · Answer

ohhhhh

anonymous · Answer

i gotcha now

anonymous · Answer

Thank you!!!!!!

freckles · Answer

np