ThatQuiz Test Library Take this test now
DEQUAT MIDTERM
Contributed by: Sonio
  • 1. Find the solution to y'=8y differential equation
A) y=Ce8x
B) y=82+c
C) y=8ecx
D) y=8×+c
E) y=4x2 + C
  • 2. Find the differential equation whose general solution is y = c sin x , where c is an arbitrary constant.
A) y' cosx - ycosx = 0
B) none
C) y' sinx - ycosx = 0
D) y" sinx - ycosx = 0
E) sinx - cosx = 0
  • 3. Eliminate the c on the equation cy2 = x2+y to form a differential equation.
A) 2xydx - (y -2x2)dy = 0
B) 2xydx - (y+ 2x2)dy = 0
C) 2xydx - (y+2x2)dy = 0
D) 2xdx +(y+2x2)dy = 0
E) 2xydx + (y+ 2x2)dy = 0
  • 4. Determine the differential equation whose general solution is y = c1ex + c2e^-x+ 2x.
A) y"-y -2x3= 0
B) none
C) y" + y + 2x = 0
D) y" - y + 2x = 0
E) y" - y - 2x = 0
  • 5. What type of DE is the equation d2u/ax2 + a2u/dy2 = 0.
A) Exact DE
B) Partial DE
C) Ordinary DE
D) Linear DE
E) none
  • 6. What is the order of a differential equation?
A) The number of variables in the equation.
B) The highest order derivative appear on the equation
C) The number of constants in the equation.
D) none
E) The degree of the equation.
  • 7. Eliminate the arbitrary constant c1 and c2 on the equation x=c1coswt+c2sinwt
A) x"= 0
B) w2x=0
C) x" - w2x = 0
D) x"+ w = 0
E) x" + w2x =0
  • 8. Find the differential equation whose general solution is y= c0+ c1x+ c2x2+ c3x3
A) 2x-3y=0
B) y"=0
C) y"+y=0
D) none
E) y" - y' + 6y = 0
  • 9. Solve the differential equation dy/dx = 6y2x
A) 1/y=3x2+c
B) -1/y=3x+c
C) y' =3x2 + c
D) -1/y=3x2 + c
E) -y=3x2 + c
  • 10. Which of the following are not included in steps in solving variable separable differential equation.
A) Add constants if needed
B) Integrate one side with respect to y and the other side with respect to x.
C) Move all the y terms (including dy) to one side of the equation and all the x terms (including dx) to the other side.
D) none
E) Simplify
  • 11. If you have a second-order differential equation, how many times will you need to integrate it to find the dependent variable?
A) It depends on the equation
B) none
C) twice
D) three times
E) once
  • 12. What is the order of the differential equation d3y/dx3 - d2y/dx2 + dy/dx = 0?
A) 1
B) 2
C) 0
D) none
E) 3
  • 13. In a differential equation, the variable that you're trying to solve for is called the:
A) Dependent variable
B) Independent variable
C) undefined
D) none
E) Independent variable
  • 14. Eliminate c from the equation cxy + c2x + 4 = 0
A) none
B) x3y2 - x2yy' + 4 = 0
C) x3 (y')2 + x2yy'= 0
D) x3 (y')2 + x2yy' + 4 = 0
E) x2yy'+ 4 = 0
  • 15. Find the differential equation whose general solution is y = c1e-2x+c2e3x
A) y' - 6y = 0
B) 6y = 0
C) y" - y' + 6y = 0
D) y" - y' - 6y = 0
E) y" + y' + 6y = 0
  • 16. What is the order and degree of the DE (y )8 + (y')20 = 0
A) 20th order, fourth degree
B) fourth order, first degree
C) none
D) third order, 20th degree
E) first order, 20th degree
  • 17. What type of DE is the equation d2y/dx2 + 4dy/dx + 4y = 0
A) Linear DE
B) Partial with a 2nd order DE
C) Ordinary with a 2nd degree DE
D) Ordinary DE
E) none
  • 18. What type of DE is the equation d2y/dx2 + 4dy/dx + 4y = 0
A) Partial with a 2nd order DE
B) none
C) Linear DE
D) Ordinary DE
E) Ordinary with a 2nd degree DE
  • 19. What is the degree of the differential equation d2y/dx2 + 3(dy/dx)2 = 6?
A) 4
B) 3
C) 0
D) 1
E) 2
  • 20. What type of DE is the equation d2u/ax2 + a2u/ay2 = 0.
A) Exact DE
B) None
C) Partial DE
D) Linear DE
E) Ordinary DE
Created with That Quiz — the site for test creation and grading in math and other subjects.