differential equation

Timson28

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Sep 6, 2020
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I solved this differential equation but I'm not sure if I'm right.

Would you check it?

Thanks in advance
 

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Try to plug the solution in the original equation, the same way you would verify solutions of a “normal” (for example linear) equation, see what will you get.
 
First note that ea+b=eaeb\displaystyle e^{a+ b}= e^ae^b so you can write your solution as
y=ec1ex1\displaystyle y= e^{c_1}e^{-x}- 1.

And, since c1\displaystyle c_1 is an arbitrary constant, so is ec1\displaystyle e^{c_1} so let C=ec1\displaystyle C= e^{c_1} and
y=Cex1\displaystyle y= Ce^{-x}- 1.

Now, y=Cex\displaystyle y'= -Ce^{-x} so what is y+xy+x\displaystyle y'+ xy+ x?
 
[MATH]\frac{dy}{dx} = -x(y+1)[/MATH]
[MATH]\frac{dy}{y+1} = -x \, dx[/MATH]
now integrate …
 
I solved this differential equation but I'm not sure if I'm right.

Would you check it?

Thanks in advance
The best way to check your answer is:

Differentiate the function you derived and see whether that satisfies the given DE.​
 
I solved this differential equation but I'm not sure if I'm right.

Would you check it?

Thanks in advance
The left side has x and the right side has y'. How does that change to dx on the left and dy on the right? Try "multiplying" both sides by dx
 
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