Differential Equation Problem

Question

anonymous · Answer

That's a good one.

anonymous · Answer

attachment

anonymous · Answer

Obtain the general solution of the following differential equation by integrating factors found by inspection

abb0t · Answer

This kind of looks like an exact equation.

anonymous · Answer

The instruction said that we should use integrating factors found by inspection

psymon · Answer

Not sure about the whole by inspection thing, but I do not think that it means we need to solve this in some sort of special way. Do you know about some of the basic substitutions that are used to help separate variables?

anonymous · Answer

some are exact equations, Bernoulli's equation, linear equations, substitution suggested by the equation?

anonymous · Answer

well this is a Bernoulli equation

psymon · Answer

Can this not be done with the substitutions of y = vx and dy = vdx + xdv?

anonymous · Answer

The instruction said that we should use integrating factors found by inspection

anonymous · Answer

The solution to
$$y(x) \left(3 x^3+y(x)-x\right)+\left(1-x^2\right) x^2 y'(x)=0  $$is$$y(x)=\frac{x-x^3}{c_1+\log (x)} $$Solved by Mathematica and WolframAlpha.com .
Neither program provides the solution steps.

anonymous · Answer

tnx everyone & @robtobey