How to Solve Differential Equations with Wolfram Alpha?

[flyingpig]

Homework Statement

i can solve them myself, but sometimes I am just lazy.

How do you make Wolframalpha solve these exact, non-exact, other ODEs?

Ex.

$$2y^2 + 2y + 4x^2 + (2xy + x)y' = 0$$

I tried using

DSolve[{(2*y[x]^2 + 2y[x] + 4x^2) + (2xy[x] + x)y'[x] = 0 }, y[x], x]

Not working?Problem

Solve $$2y^2 + 2y + 4x^2 + (2xy + x)y' = 0$$

Work

$$\frac{\partial }{\partial y}(2y^2 + 2y + 4x^2) = 4y + 2$$

$$\frac{\partial }{\partial x}(2xy + x) = 2y + 1$$

$$\frac{4y+2-2y - 1}{2xy + x} = \frac{2y+1}{x(2y+1)} = \frac{1}{x}$$

Then clearly the integrating factor is $$\mu (x) = x$$

Now my question is, what is the solution that is lost? Is it y = -1/2? Because of $$\frac{2y+1}{x(2y+1)}$$?

 

[cristo]

The good thing about wolfram|alpha is that you don't need to use correct notation. I just typed in "solve 2y^2+2y+4x^2+(2xy+x)dy/dx=0" and it worked.

 

[flyingpig]

How do you make it show your solutions implicity?

 

[HallsofIvy]

Do you tell your teacher that you use Wolfram alpha to solve homework problems?

 

[flyingpig]

Do you tell your teacher that you use Wolfram alpha to solve homework problems?

No self-studying right now, but I use it for problems that I don't have the solutions to. The instructor manual I got for some reason only has even solutions.

That's why I am using computers to replace them now lol