The general solution of the differential equation 100d2ydx2-20dydx+y=0is
y=(c1+c2x)ex
y=(c1+c2x)e-x
y=(c1+c2x)ex10
y=c1ex+c2e-x
Find the general solution of the differential equation.
Given,100d2ydx2-20dydx+y=0
Put D=ddx
⇒(100D2-20D+1)y=0⇒100D2-20D+1=0⇒100D2-10D-10D+1=0⇒10D(10D-1)-1(10D-1)=0⇒(10D-1)2=0⇒D=110,110
Since, roots are real and equal.
∴General Solution is y=(c1+c2x)ex10
Hence, option (C) is the correct answer.