This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 27 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 27 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The formula for cos (A +B) is A) Cos A cos B + sin A sin B. B) Sin A cos B + cos A sin B. C) Sin A cos B-cos A sin B. D) Cos A cos B-sin A sin B. Show Answer Correct Answer: D) Cos A cos B-sin A sin B. 2. The annihilator of eax is A) D-a. B) D + a. C) D2-a. D) D2+a. Show Answer Correct Answer: A) D-a. 3. The particular solution of the differential equation $\left(x^2+1\right)\frac{\text{d}y}{\text{d}x}+xy=x\left(x^2+1\right)$ A) $y=\frac{1}{3}\left(x^2+1\right)^{\frac{3}{2}}-\frac{1}{3}$. B) $y=\frac{x^2\left(x^2+2\right)}{4\left(x^2+1\right)}$. C) $y=\frac{1}{3}\left(x^2+1\right)-\frac{1}{3}\left(x^2+1\right)^{-\frac{1}{2}}$. D) $y=\frac{1}{3}\left(x^2+1\right)+\frac{1}{3}\left(x^2+1\right)^{\frac{1}{2}}$. Show Answer Correct Answer: C) $y=\frac{1}{3}\left(x^2+1\right)-\frac{1}{3}\left(x^2+1\right)^{-\frac{1}{2}}$. 4. What is the Frobenius method used for? A) To solve linear equations. B) To find power series solutions. C) To determine the Wronskian. D) To solve non-homogeneous equations. Show Answer Correct Answer: B) To find power series solutions. 5. Apa bentuk umum dari persamaan diferensial linear homogen orde kedua? A) Y" + y' + c = 0. B) A(x)y" + b(x)y' + c(x)y = 0. C) Y" + b(x)y' + c(x)y" = 0. D) A(x)y" + b(x)y' + y = 0. Show Answer Correct Answer: B) A(x)y" + b(x)y' + c(x)y = 0. 6. The difference between a particular solution to a separable differential equation and a general solution is that in a particular solution you must ..... A) Solve for C. B) Separate the variables. C) Integrate. D) Use $\ln$. Show Answer Correct Answer: A) Solve for C. 7. Find the general solution. $\frac{dy}{dx}=6xy$ A) $y=\sqrt[]{6x^2+C}$. B) $y=\ln\left(3x^2+C\right)$. C) $y=Ce^{3x^2}$. D) $y=Ce^{6x}$. Show Answer Correct Answer: C) $y=Ce^{3x^2}$. 8. In the steady state, the change in temperature at any point with respect to time is A) 0$^{0}$C. B) >0$^{0}$C. C) <0$^{0}$C. D) None of these. Show Answer Correct Answer: A) 0$^{0}$C. 9. The general solution of the DE $\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}-5y=0$ A) $y=Ae^x+Be^{-5x}$. B) $y=Ae^{-x}+Be^{5x}$. C) $y=Ae^x+Be^{5x}$. D) $y=Ae^{-x}+Be^{-5x}$. Show Answer Correct Answer: A) $y=Ae^x+Be^{-5x}$. 10. $L^{-1}\left[F'\left(s\right)\right]=$ A) $xL^{-1}\left[F\left(s\right)\right]$. B) $-xL^{-1}\left[F\left(s\right)\right]$. C) $-\frac{d}{ds}\left[F\left(s\right)\right]$. D) $-\frac{d}{ds}\left[xF\left(s\right)\right]$. Show Answer Correct Answer: B) $-xL^{-1}\left[F\left(s\right)\right]$. 11. The general solution of the differential equation $\frac{\text{d}y}{\text{d}x}=2xy$ A) $y=e^{x^2}+A$. B) $y=Ae^{x^2}$. C) $y=e^{x^2}$. D) $y=\ln\left(x^2+A\right)$. Show Answer Correct Answer: B) $y=Ae^{x^2}$. 12. What is the first step in solving differential equations using separation of variables? A) Separate variables to different sides. B) Solve for the constant of integration. C) Apply implicit differentiation. D) Integrate both sides immediately. Show Answer Correct Answer: A) Separate variables to different sides. 13. What are slope fields used for in differential equations? A) Studying chemical reactions. B) Graphing linear equations. C) Solving algebraic equations. D) Visualizing the behavior of solutions to differential equations. Show Answer Correct Answer: D) Visualizing the behavior of solutions to differential equations. 14. The general solution to $e^y\\frac{dy}{dx}=3x^2$ A) $e^y=6x+c$. B) $Ae^y=x^3+c$. C) $y=e^y+6x+c$. D) $e^y=x^3+c$. Show Answer Correct Answer: D) $e^y=x^3+c$. 15. Suppose that a cup of coffee begins at 183 degrees and, after sitting in room temperature of 69 degrees for 19 minutes, the coffee reaches 173 degrees. How long will it take before the coffee reaches 163 degrees? A) 38 minutes. B) 28 minutes. C) 48 minutes. D) 58 minutes. Show Answer Correct Answer: B) 28 minutes. 16. The solution of the equation z = px + qy + pq is ..... A) Z = ax + by + pq. B) Z = ax + by + ab. C) Z = bx + ay + ab. D) Z = px + qy + ab. Show Answer Correct Answer: B) Z = ax + by + ab. 17. Identify the type of PDE:u ..... xx-u ..... yy = 0. A) Elliptic. B) Parabolic. C) Linear. D) Hyperbolic. Show Answer Correct Answer: D) Hyperbolic. 18. Find the solution to dy/dx = sin(x) with y(0) = 1. A) Y =-cos(x) + 2. B) Y =-sin(x) + 1. C) Y = cos(x) + 1. D) Y = sin(x) + 1. Show Answer Correct Answer: A) Y =-cos(x) + 2. 19. What is the main purpose of the method of variation of parameters? A) To determine the Wronskian. B) To solve linear equations. C) To find a particular solution of a non-homogeneous equation. D) To find the general solution of a homogeneous equation. Show Answer Correct Answer: C) To find a particular solution of a non-homogeneous equation. 20. L$^{-1 }$\{n!/(s-a)$^{n+1}$\} A) 1. B) T$^{n}$. C) E$^{at}$. D) T$^{n }$e$^{at}$. E) Cos bt. Show Answer Correct Answer: D) T$^{n }$e$^{at}$. 21. $7x=\int3x++2dx_{ }^{ }$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: B) NO. 22. Which of the following differential equations can NOT be solved by separation of the variables? A) $\frac{dy}{dx}=x$. B) $\frac{dy}{dx}=\frac{x}{y}$. C) $\frac{dy}{dx}=xy$. D) $\frac{dy}{dx}=x+y$. Show Answer Correct Answer: D) $\frac{dy}{dx}=x+y$. 23. Find a particular solution for:y" -3y' + 2y = e$^{x}$ A) Xe$^{2x}$. B) 2 xe$^{x}$. C) -xe$^{x}$. D) E$^{x}$. Show Answer Correct Answer: C) -xe$^{x}$. 24. What is the order of a differential equation that involves finding the solution at a specific point? A) First order. B) Second order. C) Third order. D) Higher order. Show Answer Correct Answer: A) First order. 25. Sketch the slope field for the differential equation dy/dx = x-y A) Slope field sketching is a visual process and cannot be represented as a single correct answer. B) The slope field is a parabola. C) The slope field is a straight line. D) The slope field cannot be sketched for this differential equation. Show Answer Correct Answer: A) Slope field sketching is a visual process and cannot be represented as a single correct answer. ← 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 5Class 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 10 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books