This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 5 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following equations has complex roots in its characteristic equation? A) $y" + 2y' + y = 0$. B) $y" + 4y = 0$. C) $y" -6y' + 9y = 0$. D) $y" -2y' + y = 0$. Show Answer Correct Answer: B) $y" + 4y = 0$. 2. If the number of constants to be eliminated is greater than the number of independent variables, then the result is ..... A) First order PDE. B) Second and higher order PDE. C) Second and higher order PDE. D) Only Second order linear PDE. Show Answer Correct Answer: B) Second and higher order PDE. 3. What is the general solution to the DE $\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0$ A) $y=Ce^{-x}+De^{8x}$. B) $y=Ce^x+De^{-8x}$. C) $y=Ce^x+De^{7x}$. D) $y=Ce^{-x}+De^{7x}$. Show Answer Correct Answer: B) $y=Ce^x+De^{-8x}$. 4. Polynomials are not analytic at all points. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 5. The general solution of a first-order PDE is: A) A function of arbitrary functions of the variables involved. B) A polynomial function of fixed coefficients. C) A linear combination of the variables only. D) A constant function of the variables involved. Show Answer Correct Answer: A) A function of arbitrary functions of the variables involved. 6. If Eigen values of a matrix are 0, 1, 2, then the matrix will be A) Non-singular. B) Singular. C) Both. D) None of these. Show Answer Correct Answer: B) Singular. 7. Solve dy/dx = x(y+5) A) $y=Ce^{\frac{1}{2}x^2}+5$. B) $y=Ce^{\frac{1}{2}x^2}-5$. C) $y=5e^{\frac{1}{2}x^2}-C$. D) $y=\frac{Ce^{\frac{1}{2}x^2}}{e^5}$. Show Answer Correct Answer: B) $y=Ce^{\frac{1}{2}x^2}-5$. 8. What is the general form of a second order ordinary differential equation (ODE)? A) Y" + y' + y = 0. B) Y" + 2y' + y = f(t). C) A y" + b y = 0. D) A y" + b y' + c y = f(t). Show Answer Correct Answer: D) A y" + b y' + c y = f(t). 9. Find the particular solution to the differential equation $\frac{dy}{dx}=\frac{2xy}{x^2+1}$ $\left(1, \-2\right)$ A) $y=3e^{2x^3}$. B) $y=-x^2-2$. C) $y=x^2+1$. D) $y=-x^2-1$. Show Answer Correct Answer: D) $y=-x^2-1$. 10. What is the definition of a separable differential equation? A) An equation containing the derivatives of one or more unknown functions with respect to one or more independent variables. B) A differential equation with separable variables. C) A differential equation where the unknown function depends on only one independent variable. D) An nth-order ordinary differential equation in one dependent variable. Show Answer Correct Answer: B) A differential equation with separable variables. 11. Apa metode untuk menyelesaikan persamaan diferensial homogen orde kedua dengan koefisien konstan? A) Integrasikan persamaan secara langsung untuk menemukan solusi. B) Gunakan metode numerik untuk mendekati solusi. C) Gunakan transformasi Laplace untuk menyelesaikan persamaan. D) Gunakan persamaan karakteristik untuk menemukan akar dan membangun solusi umum. Show Answer Correct Answer: D) Gunakan persamaan karakteristik untuk menemukan akar dan membangun solusi umum. 12. The particular integral of (D$^{2}$-9)y=cos3x is ..... A) Cos3x/18. B) Cos3x/9. C) Cos3x/-18. D) None of these. Show Answer Correct Answer: C) Cos3x/-18. 13. Which of the following is the solution to the differential equation $y^{" }-4y=0$ A) $y=e^{-4x}$. B) $y=2x^2$. C) $y=e^{2x}$. D) $y=e^{2x^2}$. Show Answer Correct Answer: C) $y=e^{2x}$. 14. $\left(\frac{dy}{dx}\right)^2+5\\frac{dy}{dx}+6=0$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 15. Solve the initial value problem. y" = $xe^{2x}$ A) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x}-3$. B) Y = $\frac{1}{4}xe^{2x} + \frac{1}{8}e^{2x}-3$. C) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x} + 3$. D) Y = $\frac{1}{4}xe^{2x} + \frac{1}{8}e^{2x} + 3$. Show Answer Correct Answer: A) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x}-3$. 16. L\{(1/48b$^{6}$)((15-6(bt)$^{2}$sin bt-(15bt-(bt)$^{3}$)bt cos bt)\} A) B/(s$^{2}$+b$^{2}$). B) B/(s$^{2}$+b$^{2}$)$^{2}$. C) B/(s$^{2}$+b$^{2}$)$^{3}$. D) B/(s$^{2}$+b$^{2}$)$^{4}$. Show Answer Correct Answer: D) B/(s$^{2}$+b$^{2}$)$^{4}$. 17. State TWO types of solutions of Differential Equations A) General Solutions Only. B) General and Particular Solutions. C) Particular Solutions Only. D) No solutions. Show Answer Correct Answer: B) General and Particular Solutions. 18. $\frac{\text{d}^2y}{\text{d}x^2}-2\frac{\text{d}y}{\text{d}x}+y=0$ A) $y=Ae^x$. B) $y=Axe^{-2x}$. C) $y=e^x\left(A+Bx\right)$. D) $y=Ae^x+Bx$. Show Answer Correct Answer: C) $y=e^x\left(A+Bx\right)$. 19. The roots of m$^{3}$ + 3m$^{2}$ + 3m +1 = 0 are A) 1, 1, -1. B) 1, 1, 1. C) 1, 0, 1. D) 1, 2, 3. Show Answer Correct Answer: B) 1, 1, 1. 20. Determine the general solution of $9y"+6y'+y=0$ A) $y=C_1e^{-\frac{x}{3}}+C_2xe^{-\frac{x}{3}}$. B) $y=C_1e^{-\frac{x}{3}}+C_2e^{-\frac{x}{3}}$. C) $y=e^{-\frac{x}{3}}\left(C_1\cos x+C_2\sin x\right)$. D) $y=e^x\left(C_1\cos\frac{x}{3}+C_2\sin\frac{x}{3}\right)$. Show Answer Correct Answer: A) $y=C_1e^{-\frac{x}{3}}+C_2xe^{-\frac{x}{3}}$. 21. Milne's method consists of: A) Only predictor. B) Only corrector. C) Predictor and corrector. D) Taylor expansion. Show Answer Correct Answer: C) Predictor and corrector. 22. Can you explain the concept of boundary conditions in the context of partial differential equations? A) Boundary conditions define the behavior of the solution at the boundaries of the domain. B) Boundary conditions have no impact on the solution. C) Boundary conditions only apply to ordinary differential equations. D) Boundary conditions are only relevant for linear equations. Show Answer Correct Answer: A) Boundary conditions define the behavior of the solution at the boundaries of the domain. 23. What is the general form of a first-order PDE? A) F(x, y, u, q) = 0. B) F(x, y, u) = 0. C) F(x, y, u, p) = 0. D) F(x, y, u, p, q) = 0. Show Answer Correct Answer: D) F(x, y, u, p, q) = 0. 24. State the order and degree of this following Differential Equations $\left(\frac{\text{d}^3x}{\text{d}y^3}\right)^5+xy=1-x$ A) Order=5Degree=3. B) Order=1Degree=1. C) Order=1Degree=0. D) Order=3Degree=5. Show Answer Correct Answer: D) Order=3Degree=5. 25. $\frac{dy}{dx}+x^2y=\left(xy\right)^3$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: C) Bernoulli. ← PreviousNext →Related QuizzesClass 12 Mathematics Chapter 9 Differential Equations Quiz 1Class 12 Mathematics Chapter 9 Differential Equations Quiz 2Class 12 Mathematics Chapter 9 Differential Equations Quiz 3Class 12 Mathematics Chapter 9 Differential Equations Quiz 4Class 12 Mathematics Chapter 9 Differential Equations Quiz 6Class 12 Mathematics Chapter 9 Differential Equations Quiz 7Class 12 Mathematics Chapter 9 Differential Equations Quiz 8Class 12 Mathematics Chapter 9 Differential Equations Quiz 9Class 12 Mathematics Chapter 9 Differential Equations Quiz 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books