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標題:

MATHS!

發問:

i) verify that y=cx+1/c is the general solution of the non-linear differential equation y(dy/dx)=x(dy/dx)^2+1

最佳解答:

y = cx + 1/c y' = c yy' - x(y')2 - 1 = cy - c2x - 1 = c(cx + 1/c) - c2x - 1 = 0 So yy' = x(y')2 + 1

其他解答:

dy/dx =c Left Hand side: y(dy/dx) = cy=c(cx+1/c) =xc^2+1 Right hand side=x (dy/dx)^2+1 =xc^2+1 Left hand side = right hand side So, y=cx+1/c is the general solution of the non-linear differential equation

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