CSIR-NET Mathematical Science - ODE & PDE MCQ - Attempt Here!

ODE & PDE MCQ 

Question 1-

1.  2x²y² = –1
2. 4x⁴y = – 1
3. 2xy⁴ = –1
4. 4x⁴y⁴ = –1

    

   Question 2- Using the method of variation of parameters, the particular integral  of the differential equation  can be expressed as , where A(x) and B(x) are given by

    

   A. (x) = 

   B. 

   C. 

   D. 

    

   Question 3- 

   The general solution of the differential equation  is of the form F(u, v) = 0 where u(x, y, z) = C₁ and v(x, y, z) = C₂ are given by

   A. 

   B. 

   C. 

   D. 

    

   Question 4- 

    

   For x = r cos q, y = r sin q, which of the following is/are correct

    

   A.  

   B. 

   C.  

   D. 

    

   Question 5-

    

   Let u (x, t) be the solution of u_tt = u_xx: 0 < x < 1, t > 0, u(x, 0) = x(1 + x), u_t(x_­, 0) = 0 then

    

   A. u (1, 0) = 4

    

   B. 

    

   C. u (1, 0) = 2

    

   D. 

    

   Question 6-

    

   For the differential equation

   

   A. x = 1 is an ordinary point

    

   B. x = 1 is a regular singular point

   
   

   C. x = 0 is an irregular singular point

    

   D. x = 0 is an ordinary point

    

    Question 7- 

   The general solution of the system of differential equations

    is given

    

   A.  : 

   B.  : 

   C.  : 

   D.  : 

    

   Question 8- 

    

   Let  be solutions of y” – 2xy + (sin x²) y = 0 such that  & . Then the value of the Wronskian  at x = 0 is-

    

   A. 0

   B. 1

   C. E

   D. None

    

   Question 9- 

    

   The general solution  of the system x’ = -x + 2y & y’ = 4x + y is given by

    

   A. 

   B. 

   C. 

   D. 

    

    Question 10-

    

   Which of the following is/are false for the partial differential equation

   

   A. Elliptic in the region x < 0, y < 0, xy > 1

   B. Elliptic in the region x > 0, y > 0, xy > 1

   C. Parabolic in the region x < 0, 4 < 0, xy > 1

   D. Hyperbolic in the region x < 0, y < 0, xy > 1