Is this ok ?

[owoc]

Hello, can you check my mathematical solutions ? I solved tasks, but I don't know if it's good. Can you check if it's okay?

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[HallsofIvy]

You can always check them by talking the derivative of the presumed solution and putting them in the equation. In the first one, I will say that that u= y/x is the correct substitution. Then y= xu so y'= u+ xu'. The differential equation becomes xu'+ u= e^u+ u so xu'= e^u. e^{-u}du= dx/x. Integrating both sides, -e^{-u}= -e^{-y/x)= ln(x)+ C.

 

[Steven G]

2nd sheet of paper. The last line is wrong.

I agree with HallsofIvy that you can check your answers by simply differentiating your answer.