Second Order Linear ODE

Second Order Linear ODE

University - Professional Development

10 Qs

quiz-placeholder

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Second Order Linear ODE

Second Order Linear ODE

Assessment

Quiz

Mathematics

University - Professional Development

Practice Problem

Hard

Created by

Divya S

Used 16+ times

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the general solution to the DE d2xdy2+7dxdy8y=0\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0  ?

 y=Cex+De8xy=Ce^{-x}+De^{8x}  

 y=Cex+De8xy=Ce^x+De^{-8x}  

 y=Cex+De7xy=Ce^x+De^{7x}  

 y=Cex+De7xy=Ce^{-x}+De^{7x}  

2.

MULTIPLE SELECT QUESTION

1 min • 1 pt

 d2xdy2+4dxdy6y=0\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}-6y=0  

Which of the following options are TRUE about the above DE?

The roots of the auxiliary equations are two complex roots.

The auxiliary equation has two different roots.

The auxiliary equation has two equal roots.

The equation is homogeneous.

3.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given  d2xdy2+4dxdy+3y=2ex.\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}+3y=2e^{-x}.  

The correct  ypy_p  is

 CexCe^{-x}  

 Ccosx+DsinxC\cos x+D\sin x  

 CexCe^x  

 CxexCxe^{-x}  

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

 d2xdy2y=cotx\frac{\text{d}^2x}{\text{d}y^2}-y=\cot x  
The above DE can be solved using the undetermined coefficient meThod.

TRUE

FALSE

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find a general solution of the following homogeneous linear second order differential equation.

y "- 2 y '- 8 y=0

y = c1e2x + c2e4x

y= c1e-2x + c2e4x

y = c1e2x + c2e-4x

y = c1e-2x + c2e-4x

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The following non-homogeneous linear second order ODE has yh=c1ex+c2xex . What is its yp if it is to be solved using Undetermined Coefficient Approach?


y "-2 y '+ y = xex

(1/6)(x3ex)

(1/6)(xex)

(1/6)(x2ex)

x3ex

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Find the characteristics equation for y"+4 y'+4 y= 2x + 6.

m2+4m+4=0

m2+4m+4=2x+6

m2+4m=0

m2+4=0

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