solve the equation:

this is a tough problem for me that i cant start...

i can't find any separable nor any linearity in this solution

ill try to solve

solution:

substitute let w = sin(y)

dw = cos(y)dy so substitute

....

now im stuck

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- Jan 9th 2008, 04:37 AM^_^Engineer_Adam^_^Bernoulli's equation
solve the equation:

this is a tough problem for me that i cant start...

i can't find any separable nor any linearity in this solution

ill try to solve

solution:

substitute let w = sin(y)

dw = cos(y)dy so substitute

....

now im stuck - Jan 9th 2008, 05:30 AMTwistedOne151Further transform
Let us define another change of variable for our dependent variable: choose .

Then , , and thus our equation becomes

This is a nonhomogenous first order linear differential equation. We can see by substitution that is a solution. Thus, we find and add to that the general solution for the corresponding homogenous equation

, which is separable:

Thus the solution to is , and from there you can convert back into w, and then into .

--Kevin C.