Differential Equations: x dy/dx+x^2=5, xy+x^2=5

[Guest]

could someone explain if i have done this work example right as it would help me understand abit better?

x dy/dx+x^2=5

xy+x^2=5

y=5-x^2/x

y=5-x^2/x dx

∫(5-x^2)/x dx=5 ln⁡(x)-x^2/2+c_1

y=5 ln⁡(x)-x^2/2+c_1

[Guest]

could someone explain if i have done this work example right as it would help me understand abit better?

x dy/dx+x^2=5

xy+x^2=5

y=5-x^2/x

Ouch! I have a strong desire to whack you over the head! You are probably doing this correctly but writing it very badly. Going from x dy/dx+ x^2= 5 to xy+ x^2= 5, what happened to the derivative? How did dy/dx turn into y? And 5- x^2/x is equal to 5- x, NOT (5- x^2)/x. From x dy/dx+ x^2= 5 you can go to x dy/dx= 5- x^2 then dy/dx= (5- x^2)/x= 5/x- x.

y=5-x^2/x dx

This is the same as the line before- I don't understand why you wrote it again. And it should be dy= [(5- x^2)/x] dx

∫(5-x^2)/x dx=5 ln⁡(x)-x^2/2+c_1

Yes! Finally you have written something correctly- even with the parentheses! Hooray!
[tex]\int (5- x^2)/x dx= \int \frac{5}{x}- x dx= 5ln(x)- \frac{x^2}{2}+ c_1[/tex].

y=5 ln⁡(x)-x^2/2+c_1