Which of the following differential equations has two real and equal roots? Select one: a. d2ydx2=4y b. 16d2ydx2−8dydx+y=0 c. 3d2ydx2+2dydx=0 d. d2ydx2=−4y

Name: Which of the following differential equations has two real and equal roots? Select one: a. d2ydx2=4y b. 16d2ydx2−8dydx+y=0 c. 3d2ydx2+2dydx=0 d. d2ydx2=−4y
Uploaded: 2022-02-23T17:22:57+00:00
Description: Which of the following differential equations has two real and equal roots? Select one: a. d2ydx2=4y b. 16d2ydx2−8dydx+y=0 c. 3d2ydx2+2dydx=0 d. d2ydx2=−4y

Question

Which of the following differential equations has two real and equal roots? Select one:  a. d2ydx2=4y  b. 16d2ydx2−8dydx+y=0  c. 3d2ydx2+2dydx=0  d. d2ydx2=−4y

Pademagk71 · Accepted Answer

Here roots of differental equations means roots of auxilary equation    A quadratic equation ax2+bx+c=0 has real and equal root  if and only if D=b2−4ac=0  a) d2ydx2=4y  Auxilary equation m2−4=0  and roots are m=2,−2 real but bot equal  b) Auxilary equation  16m2−8m+1=0  a=16.b=−8 c=1  D=b2−4ac  D=64−64=0  hence equation 16d2ydx2−8dydx+y=0  has equal and real roots  c) Auxiliary equation; 3m2+2m=0  has roots m=0,−23; real but not equal  d) Auxilary equation: m2=−4; No real roots  so, only equation in option B has real and equal roots  Therefore correct choice is option B

lalilulelo2k3eq · Accepted Answer

a) d2ydx=4y  d2ydx2−4y=0  r2−4=0  r2=4⇒r=±2⇒r=2,−2  so, roots are real  b) 16d2ydx2−8dydx+y=0  The auxilliary eq.  16r2−8r+1=0  (4r−1)2=0  4r−1=0⇒2=14,14  Here root but roots are real.  c) d2ydx2=−4y  d2ydx2+4y=0  The auxilliary eq  r2+4=0  r2=−4  r=±−4  r=±2−1,∴−1=i  r=±2i⇒r=2i,−2i  so, roots are complex  3d2ydx2+2dydx=0  the auxilliary eq  3r2+2r=0  r(3r+2)=0⇒r=0,r=−33  root are real  Answer: Option c is correct

alenahelenash · Accepted Answer

Differential equation, characteristic equation a) 16D2−8D+1=0 b2−4ac⇒(−8)2−4(16)(2) =64−64 =0 Differential equation has two real and equal root b) D2=4⇒D2−4=0 D=±2 c) 3D2+2D=0 D(3D+2)=0⇒D=0 and D=−23 Differential equation has two real roots but not equals d) D2=−4 D=±2 So differential equation has complex roots Therefore option (a) is the correct answer a. 16dydx2−8dydx+y=0

Which of the following differential equations has two real and

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