Question

CQ (100)
Q7. The differential equation whose auxiliary equation has
the roots 0,-1,-1 is
(A)
dy = 0
223
(B) dy
day
= 0
(C) day
dy = 0
+
(D) ay
dia3
+ dy = 0
+ 2013​

Answer 1

Answer:

CQ (100)

Q7. The differential equation whose auxiliary equation has

the roots 0,-1,-1 is

(A)

dy = 0

223

(B) dy

day

= 0

(C) day

dy = 0

+

(D) ay

dia3

+ dy = 0

+ 2013

Answer 2

Answer:

The differential equation whose auxiliary equation has the roots 0,-1,-1 is    $\frac{d^3y}{dx^3} -2\frac{d^2y}{dx^2}+\frac{dy}{dx}=0$

Step-by-step explanation:

• The roots of the Auxilary equation are also the roots of the equation.
• The auxilary equation roots are 0,-1,-1.
• Thus, the factors are

        $(x=0),(x=-1),(x=-1)\\(x-0),(x+1),(x+1)\\x,(x+1),(x+1)$

• Multiplying the factors , one can determine the auxilary equation.    

       $x(x-1)^2=0\\x(x^2+1-2x)=0\\x^3-2x^2+x=0$

• Replace x with D and multiplyby y

        $(D^3-2D^2+D)y=0\\\frac{d^3y}{dx^3} -2\frac{d^2y}{dx^2}+\frac{dy}{dx}=0$

Conclusion:

The differential equation whose auxiliary equation has the roots 0,-1,-1 is  $\frac{d^3y}{dx^3} -2\frac{d^2y}{dx^2}+\frac{dy}{dx}=0$