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
MATHS!
2009-05-13 5:50 pm
回答 (2)
2009-05-13 6:44 pm
✔ 最佳答案
y = cx + 1/cy' = c
yy' - x(y')2 - 1 = cy - c2x - 1
= c(cx + 1/c) - c2x - 1
= 0
So
yy' = x(y')2 + 1
參考: Myself
2009-05-13 6:45 pm
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
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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