How to find the general solution #(x-2)dy/dx - y = 0# ?

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Answer 1 · 2018-05-20T13:15:54

The general solution is #y=C(x-2)#

The ODE is

#(x-2)dy/dx-y=0#

#(x-2)dy/dx=y#

Therefore,

#dy/y=dx/(x-2)#

#intdy/y=intdx/(x-2)#

#lny=ln(x-2)+C_1#

#y=e^(ln(x-2)+C_1)=e^(C_1)*e^(ln(x-2))#

#y=C(x-2)#