Understanding the Role of Constants in First Order Differential Equations

[converting1]

solve dy/dx = x(1-x)

I got y = (x^2)/2 - (x^3)/3 + C

however in the solutions they've gotten:

where did t come from?

 

[Pi-Bond]

It came when they integrated dt on the right hand side, 2 steps above where you marked the solution.

 

[Dick]

It looks to me like there is a typo in the problem. y disappeared! I think they meant the derivative to be dx/dt, not dy/dx. Your solution to dy/dx=x(1-x) is correct.

 

[Pi-Bond]

Oh nice spot!

 

[pierce15]

It looks to me like there is a typo in the problem. y disappeared! I think they meant the derivative to be dx/dt, not dy/dx. Your solution to dy/dx=x(1-x) is correct.

Yeah it definitely looks like the problem was supposed to be dx/dt

 

[converting1]

thanks guys