Differential Equation problem

[lamaclass]

I wasn't sure if I had done this one correctly.

Find a particular solution to the differential equation dy/dx = (y[sup:1didk6ns]2[/sup:1didk6ns]+1)x, y(0) = 1.


My work:

IN dy/y[sup:1didk6ns]2[/sup:1didk6ns]+1 = IN x dx

= ln[y[sup:1didk6ns]2[/sup:1didk6ns]+1] = x[sup:1didk6ns]2[/sup:1didk6ns]/2 + C[sub:1didk6ns]1[/sub:1didk6ns]

y[sup:1didk6ns]2[/sup:1didk6ns]+1 = e[sup:1didk6ns]x^{2/2[/sup:1didk6ns]}-1

y(0)=1, 1=Ce[sup:1didk6ns]0[/sup:1didk6ns]-1, C=0?

 

[Deleted member 4993]

I wasn't sure if I had done this one correctly.

Find a particular solution to the differential equation dy/dx = (y[sup:w6cx61za]2[/sup:w6cx61za]+1)x, y(0) = 1.


My work:

IN dy/y[sup:w6cx61za]2[/sup:w6cx61za]+1 = IN x dx

= ln[y[sup:w6cx61za]2[/sup:w6cx61za]+1] = x[sup:w6cx61za]2[/sup:w6cx61za]/2 + C[sub:w6cx61za]1[/sub:w6cx61za] ? that is not correct. If you differentiate ln(y[sup:w6cx61za]2[/sup:w6cx61za] + 1) you would get (2*y)/(y[sup:w6cx61za]2[/sup:w6cx61za] + 1)
y[sup:w6cx61za]2[/sup:w6cx61za]+1 = e[sup:w6cx61za]x^{2/2[/sup:w6cx61za]}-1

y(0)=1, 1=Ce[sup:w6cx61za]0[/sup:w6cx61za]-1, C=0?

\(\displaystyle \int \frac{dy}{1+y^2} = tan^{-1}(y) + C\)

 

[lamaclass]

Ok got it! Thanks for your help!