MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Partial Differential Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A homogeneous linear differential equation has constant coefficients if it has the form (a_0 y+a_1 y +a_2 y + +a_n y^{(n)}=0, ) where a1, ,an are (real or complex) numbers. |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
Which of the following is not an example of linear differential equation? |
| A. | y=mx+c |
| B. | x+x =0 |
| C. | x+x<sup>2</sup>=0 |
| D. | x^ +2x=0 |
| Answer» D. x^ +2x=0 | |
| 3. |
The solution of an ODE contains arbitrary constants, the solution to a PDE contains arbitrary functions. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 4. |
What is the degree of the homogeneous partial differential equation, ( frac{ ^2 u}{ t^2}-c^2 frac{ ^2 u}{ x^2}=0 )? |
| A. | Second-degree |
| B. | First-degree |
| C. | Third-degree |
| D. | Zero-degree |
| Answer» C. Third-degree | |
| 5. |
What is the general solution of the DE with n linearly independent solutions u1(t), ., un(t) of a nth order linear homogeneous DE? |
| A. | (u(t)=u_1 (t)+ +c_{n+1} u_n (t)= _{k+1}^n=c_{k+1} u_k (t) ) |
| B. | (u(t)=u_1 (t)+ +u_n (t)= _{k=1}^nu_k(t) ) |
| C. | (u(t)=c_1 u_1 (t)+ +c_n u_n (t)= _{k=1}^n c_k u_k (t) ) |
| D. | (u(t)=c_0 u_0 (t)+ +c_n u_n (t)= _{k=0}^ c_k u_k (t) ) |
| Answer» D. (u(t)=c_0 u_0 (t)+ +c_n u_n (t)= _{k=0}^ c_k u_k (t) ) | |
| 6. |
Which of the following is not a homogeneous equation? |
| A. | ( frac{ ^2 u}{ t^2}-c^2 frac{ ^2 u}{ x^2}=0 ) |
| B. | ( frac{ ^2 u}{ x^2}+ frac{ ^2 u}{ y^2}=0 ) |
| C. | ( frac{ ^2 u}{ x^2}+( frac{ ^2 u}{ x y})^2+ frac{ ^2 u}{ y^2}=x^2+y^2 ) |
| D. | ( frac{ u}{ t} -T frac{ ^2 u}{ x^2}=0 ) |
| Answer» D. ( frac{ u}{ t} -T frac{ ^2 u}{ x^2}=0 ) | |
| 7. |
Which of the following is false regarding Bessel polynomials? |
| A. | Krall and Fink (1949) defined the Bessel polynomials |
| B. | The polynomials satisfy the recurrence formula |
| C. | The solutions of homogeneous equations are closely related to Bessel polynomials |
| D. | Bessel polynomials are not an orthogonal sequence of polynomials |
| Answer» E. | |
| 8. |
Which of the following is false regarding quasilinear equations? |
| A. | All the terms with highest order derivatives of dependent variables occur linearly |
| B. | The coefficients of terms with highest order derivatives of dependent variables are functions of only lower order derivatives of the dependent variables |
| C. | Lower order derivatives can occur in any manner |
| D. | All the terms with lower order derivatives of dependent variables occur linearly |
| Answer» E. | |
| 9. |
Homogeneous Equations are those in which the dependent variable (and its derivatives) appear in terms with degree exactly one. |
| A. | True |
| B. | False |
| Answer» B. False | |