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# Differential Equations Help watch

1. Hi,

So the question asked find general solutions of the following differential equation.

1/x dy/dx - y/x^2= 1/x^3

Multiplied both sides by x to Get :
dy/dx - y/x =1/x^2
I found out that the general solution for an equation (Attached)

I applied the formula and got y = Ln x / x + c.

The book got something completely different.

Thanks
Attached Images

2. (Original post by ChemBoy1)
Hi,

So the question asked find general solutions of the following differential equation.

1/x dy/dx - y/x^2= 1/x^3

Multiplied both sides by x to Get :
dy/dx - y/x =1/x^2
I found out that the general solution for an equation (Attached)

I applied the formula and got y = Ln x / x + c.

The book got something completely different.

Thanks
1/x dy/dx - y/x2 is the exact derivative of y*{1/x} using the product rule.

so when you integrate the LHS you get y*{1/x}
3. Thanks for this but even still, wont the above equation still work?
(Original post by the bear)
1/x dy/dx - y/x2 is the exact derivative of y*{1/x} using the product rule.

so when you integrate the LHS you get y*{1/x}
4. (Original post by ChemBoy1)
Thanks for this but even still, wont the above equation still work?
it looks like you used an Integrating Factor.... what was it ?

5. ~I've given up on differntial equations and c4 for that matter

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