Quiz II H. O. D. E.

15 Questions | By AnmaikaJain | Updated: Mar 21, 2022 | Attempts: 194

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1.

The equation d^²y/dx²+pdy/dx+qy=0 has equal roots if
- A.
  
  P²-4q>0
- B.
  
  P²>0
- C.
  
  P²-4q=0
- D.
  
  P²-q=r
2.

The solution of the differential equation d³y/dx³+ 6 d²y/dx² + 3 dy/dx -10y = 0 is
- A.
  
  C₁ e^x+C₂ e^5x +C₃ e^(-2x)
- B.
  
  C₁ e^x+C₂ e^3x +C₃ e^(-2x)
- C.
  
  C₁ e^-x+C₂ e^5x +C₃ e^(-2x)
- D.
  
  C₁ e^x+C₂ e^-2x +C₃ e^(-5x)
3.

The solution of differential equation (D^³-1)y=0 is
- A.
  
  C₁ e^x+e^(-x/2) (C₂ cos(√3x/2)+C₃ sin(√3x/2))
- B.
  
  C₁ e^-x+e^(x/2) (C₂ cos(√3x/2)+C₃ sin(√3x/2))
- C.
  
  C₁ e^x+e^(-x/2) (C₂ cos(x/2)+C₃ sin(x/2))
- D.
  
  C₁ e^x+e^-x (C₂ cos(√3x/2)+C₃ sin(√3x/2))
4.

The solution of the differential equation d²y/dx² -2 dy/dx+y=0; y(0)=0 and dy/dx (0)=1 is
- A.
  
  Xe^x
- B.
  
  0.5xe^x-0.5xe^-x
- C.
  
  Xe^x-xe^-x
- D.
  
  -xe^-0.5x
5.

The solution of the differential equation d^³y/dx³+4d^²y/dx_²-12dy/dx=0 is
- A.
  
  C₁ +C₂ e^(-6x)+C₃ e^2x
- B.
  
  C₁ e^x+C₂ e^(-4x)+C₃ e^(-2x)
- C.
  
  C₁ e^x+C₂ e^(-6x)+C₃ e^2x
- D.
  
  C₁ e^2x+C₂ e^(-6x)+C₃ e^(-2x)
6.

If f(a)=f'(a)=0 & f"(a)≠0 then P. I. of 1/f(D)e^{^ax} is
- A.
  
  1/(f" (a)) e^ax
- B.
  
  X²/(f" (a)) e^ax
- C.
  
  X/(f" (a)) e^ax
- D.
  
  X³/(f" (a)) e^ax
7.

The P. I. of the differential equation d³y/dx_³+2d²y/dx_²+dy/dx= sinx is
- A.
  
  (-1)/2 sinx
- B.
  
  1/2 sinx
- C.
  
  Sinx
- D.
  
  (-1)/2 cos x
8.

The solution of differential equation d^²y/dx²-3dy/dx-4y=e^{²^x} is
- A.
  
  C₁ e^(-x)+C₂ e^4x-1/6 e^2x
- B.
  
  C₁ e^x+C₂ e^4x-1/6 e^2x
- C.
  
  C₁ e^(-x)+C₂ e^-4x-1/6 e^2x
- D.
  
  C₁ e^(-x)+C₂ e^4x-1/6 e^-2x
9.

The solution of differential equation (D^²-6D+13)y=13 is
- A.
  
  E^3x (C₁ cos2x+C₂ sin2x)+1
- B.
  
  E^3x (C₁ cos2x+C₂ sin2x)
- C.
  
  E^x (C₁ cos2x+C₂ sin2x)+1
- D.
  
  E^-3x (C₁ cos2x+C₂ sin2x)+1
10.

The P. I. of the differential equation d³y/dx³+d²y/dx_²-dy/dx-y=cosh2x is
- A.
  
  1/18 e^2x-1/6 e^(-2x)
- B.
  
  1/18 e^2x-1/6 e^(-3x)
- C.
  
  1/9 e^3x-1/6 e^(-2x)
- D.
  
  1/18 e^2x+1/6 e^(-2x)
11.

The solution of differential equation (D^³+8)y=0 is
- A.
  
  C₁ e^(-2x)+e^x (C₂ cos(√3x)+C₃ sin(√3x))
- B.
  
  C₁ e^2x+e^x (C₂ cos(√3x)+C₃ sin(√3x))
- C.
  
  C₁ e^(-2x)+e^-x (C₂ cos(√3x)+C₃ sin(√3x))
- D.
  
  C₁ e^(-3x)+e^x (C₂ cos(√3x)+C₃ sin(√3x))
12.

The solution of the differential equation d³y/dx³-2d²y/dx²-5dy/dx+6y=0 is
- A.
  
  C₁ e^x+C₂ e^3x+C₃ e^(-2x)
- B.
  
  C₁ e^-x+C₂ e^3x+C₃ e^(-2x)
- C.
  
  C₁ e^x+C₂ e^3x+C₃ e^2x
- D.
  
  C₁ e^x+C₂ e^4x+C₃ e^(-2x)
13.

The solution of the differential equation d²y/dx₂ -dy/dx +0.25y=0; y(0)=0 and dy/dx(0)=1 is
- A.
  
  Xe^0.5x
- B.
  
  -xe^0.5x
- C.
  
  Xe^0.5x - xe^-0.5x
- D.
  
  0.5xe^-x - 0.5xe^x
14.

The solution of the differential equation d²y/dx_²-4dy/dx+4y=0 ; y(0)=0 and dy/dx (0)=1 is
- A.
  
  Xe^2x
- B.
  
  Xe^-2x
- C.
  
  Xe^0.5x-xe^-0.5x
- D.
  
  0.5xe^0.5x-0.5xe^-0.5x
15.

The solution of the differential equation d^³y/dx ³+ 2 d^²y/dx_² + dy/dx=cos x is
- A.
  
  ^{-1/2 Cos x}
- B.
  
  ^{1/2 Cos x}
- C.
  
  ^{Cos x}
- D.
  
  ^{-3/2 Cos x}