y'' + 2x (y')^2= 0

show the general solution, then find an explicit formula for a solution y(x), which also satisfies intial conditions y'(0) =1 and y (0) = 0

where to start?

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- Jan 13th 2010, 02:38 PMharveyonon-linear 2nd order differential
y'' + 2x (y')^2= 0

show the general solution, then find an explicit formula for a solution y(x), which also satisfies intial conditions y'(0) =1 and y (0) = 0

where to start? - Jan 13th 2010, 03:09 PMChris L T521
- Jan 13th 2010, 04:09 PMharveyo
seperation of variables =

u= -2x u^2

dy/dx = -2x u^2

dy/u^2 = -2x dx

integrate both sides

ln u^2 = -x^2 + C

am i doing this correct - Jan 13th 2010, 04:26 PMJhevon
- Jan 15th 2010, 05:03 PMharveyo
du/dx = -2x u^2

du/u = -2x dx

intergrate u ^-2 du = intergrate -2x dx

-u ^-1 = -x^+c - Jan 16th 2010, 04:33 AMHallsofIvy