Question

Differential Equation question: if you solve the differential equation and have all the y's and x's on different sides, but, on the side with y's you have y^2 + y ... how do you get it into y = ... form

Answer 1

Treat all the x's as a constant in the quadratic formula.

Answer 2

can u post an equation for what u r saying

Answer 3

And solve for y.

Answer 4

So if you have a general case:
\[ y^2+ay=f(x) \]
You just do:
\[ y^2+ay-f(x)=0 \]
And solve like a quadratic equation.

Answer 5

Which has the solution
\[ y=-\frac{a}{2}\pm\sqrt{f(x)+a^2/4} \]

Answer 6

I can't post the actual example as it's for a homework example. But i get what you saying with the quadratic there except it's not that easy as there are 3 terms on the side with the x's and their in the form e^x...

Answer 7

Just throw everything except the \(y^2+ay\) to the right side, which becomes \(f(x)\) and put it in the formula I derived. Maybe you can do some algebra to simplify it afterwards. But in any case it's a complete solution since you clearly get y as a function of x.