Initially w=1 Solve the differential equation to determine w at any time and wha

Question

Initially w=1

Solve the differential equation to determine w at any time and what happens to w in the long term?

I've found the solution to be stable at e^(b/a) but am having trouble going on from there.

Any help you be amazing,

Thanks

dw/dx = w(b - a * lnw) where a=1/25 and b=2/5 Initially w=1 Solve the differential equation to determine w at any time and what happens to w in the long term? I've found the solution to be stable at e^(b/a) but am having trouble going on from there. Any help you be amazing, Thanks

Explanation / Answer

solving the above linear differential equation gives the below solution ,

w = e10 - (10 / (e^(x/25)) ) .

now , the credit goes to onsolver .

follow , this link , http://onsolver.com/diff-equation.php and put " y'+(yln(y)/25)-2y/5=0 " (the given equation) in the first input and " y(0)=1 " in the second input and solve the equation .

It beautifully showed as many steps as possible and a few of its properties .

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