Help DBQ: Find solution of the given initial value problem in explicit form:
y'= (e^-x - e^x)/(3+4y), y(0)=1

Question

Help DBQ: Find solution of the given initial value problem in explicit form:
y'= (e^-x - e^x)/(3+4y), y(0)=1

perl · Answer

this equation can be separated

perl · Answer

hint, multiply both sides by 3 + 4y

anonymous · Answer

Yes and I got 3y+2y^2= -e^-x-e^x + c

anonymous · Answer

but I dont know where to go from there...

anonymous · Answer

yeah but then you have to take the integral of that, no?

abb0t · Answer

@Mimi_x3 can answer this for you.

mimi_x3 · Answer

Wow wow ....

perl · Answer

ok i agree dan

perl · Answer

3y+2y^2= -e^-x-e^x + c , 
now plug in your initial condition

anonymous · Answer

y(0)=1?

perl · Answer

y(0) = 1 

3*1 + 2*1^2 = -e^(-0) - e^(0) + C 

solve for c

anonymous · Answer

5/-2 = C?

perl · Answer

3 + 2 = -1 -1 + c 
5 = -2 + c 
5 + 2 = c

anonymous · Answer

lolz yeah 7.

anonymous · Answer

dont i have to do something with the quadratic formula?

perl · Answer

nope

perl · Answer

it will just get messy if you do

perl · Answer

hmm, it says give solution in 'explicit form'

perl · Answer

well this solution is explicit

perl · Answer

if your teacher specifically wants you to find a solution y(x)=f(x) , then yes you would have to use quadratic formula

perl · Answer

here is the solution y(x)

perl · Answer