This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 9 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 9 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the solution of ODE A) Y = Cx. B) Y = $\frac{C}{x}$. C) $y = Cx^{2}$. D) $y = Ce^{x}$. Show Answer Correct Answer: B) Y = $\frac{C}{x}$. 2. $\frac{dx}{dt}+\frac{2}{4-t}x=5$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: A) Linear. 3. What does it mean if the Wronskian of a set of functions vanishes identically? A) The functions are not defined. B) The functions are constant. C) The functions are linearly dependent. D) The functions are linearly independent. Show Answer Correct Answer: C) The functions are linearly dependent. 4. The complete integral is defined as A) The number of arbitrary constants < The number of independent variables. B) The number of arbitrary constants = The number of independent variables. C) The number of arbitrary constants > The number of independent variables. D) None of the above. Show Answer Correct Answer: B) The number of arbitrary constants = The number of independent variables. 5. What is the general solution to $y" -4y' + 13y = 0$ A) $y(x) = Ce^{2x}\sin(3x) + De^{2x}\cos(3x)$. B) $y(x) = Ce^{4x}\sin(13x) + De^{4x}\cos(13x)$. C) $y(x) = Ce^{2x} + De^{3x}$. D) $y(x) = Ce^{2x}\sin(13x) + De^{2x}\cos(13x)$. Show Answer Correct Answer: A) $y(x) = Ce^{2x}\sin(3x) + De^{2x}\cos(3x)$. 6. Consider the differential equation $\frac{dy}{dx}=\frac{x}{y}$ A) $y^2=x^2+c$. B) $y^2=\frac{x^2}{2}+c$. C) $y=x\ln\left|y\right|+c$. D) $y=\frac{x^2}{2}\ln\left|y\right|+c$. Show Answer Correct Answer: A) $y^2=x^2+c$. 7. In variation of parameters, particular solution is found by: A) Substituting constants. B) Integrating functions involving Wronskian. C) Matching coefficients. D) Separation of variables. Show Answer Correct Answer: B) Integrating functions involving Wronskian. 8. Solve the initial value problem:$y" + 2y' + 5y = 0$ $y(0) = 1$ $y'(0) = 0$ A) $y(x) = e^{-x}\cos(2x)$. B) $y(x) = e^{-x}\sin(2x)$. C) $y(x) = e^{-2x}\cos(x)$. D) $y(x) = e^{-x}\cos(2x) + e^{-x}\sin(2x)$. Show Answer Correct Answer: A) $y(x) = e^{-x}\cos(2x)$. 9. If a function is y = 2x, then its slope field equation would ..... A) Have all slopes of 2. B) Have all slopes of x$^{2}$. C) Have slopes x$^{3}$. D) Have slopes of 0. Show Answer Correct Answer: A) Have all slopes of 2. 10. Consider the general solution y = f(x) to the differential equation $\frac{dy}{dx} = \frac{y}{x}$ A) Logarithmic. B) Exponential. C) Quadratic. D) Linear. Show Answer Correct Answer: D) Linear. 11. Using the separation of variables, what is the solution of the differential equation $\frac{dy}{dx}=\frac{3xy}{1-x^2}$ A) $y=\frac{K}{\left(1+x^2\right)^{\frac{3}{2}}}$. B) $y=\frac{K}{\left(1-x^2\right)^{\frac{3}{2}}}$. C) $y=\frac{K}{\left(1-x^2\right)^{\frac{5}{2}}}$. D) $y=\frac{K}{\left(\frac{3}{2}-x^2\right)^{\frac{5}{2}}}$. Show Answer Correct Answer: B) $y=\frac{K}{\left(1-x^2\right)^{\frac{3}{2}}}$. 12. If the exact differential equation:M dx+N dy= 0 is solved using the method of integrating factors, then the integrating factor$\mu$(x, y) is chosen such that: A) $\mu$(x, y)M dx+$\mu$(x, y)N dy satisfies the exactness condition. B) $\mu$(x, y) always depends only on x. C) $\mu$(x, y) always depends only on y. D) $\mu$(x, y) must be constant. Show Answer Correct Answer: A) $\mu$(x, y)M dx+$\mu$(x, y)N dy satisfies the exactness condition. 13. The order of the following pde $\left(z_{xx}\right)^2+\left(z_{xyy}\right)+\left(z_{yy}\right)=\sin z$ A) 1. B) 2. C) 3. D) None of the above. Show Answer Correct Answer: C) 3. 14. What does the term 'particular solution' refer to? A) A solution that is always true. B) A solution that cannot be derived. C) A solution that satisfies initial conditions. D) A solution with arbitrary constants. Show Answer Correct Answer: C) A solution that satisfies initial conditions. 15. A population of flies is modeled by a function $y\left(t\right)$ $\frac{\text{d}y}{\text{d}t}=4y\left(1-\frac{y}{50}\right)$ A) 2. B) 4. C) 25. D) 50. Show Answer Correct Answer: C) 25. 16. Which of the following is a characteristic of non-linear PDEs? A) Only linear terms are present in the equation. B) The solution is always unique and stable. C) The equation can be solved using linear methods. D) Presence of non-linear terms involving the unknown function and its derivatives. Show Answer Correct Answer: D) Presence of non-linear terms involving the unknown function and its derivatives. 17. Let y=f(x) be a particular solution to the differential equation $\frac{\text{d}y}{\text{d}x}=xy^3$ $f\left(1\right)=2$ $x=1$ A) $y-2=8\left(x-1\right)$. B) $y-1=8\left(x-2\right)$. C) $y-2=2\left(x-1\right)$. D) $y-1=2\left(x-2\right)$. Show Answer Correct Answer: A) $y-2=8\left(x-1\right)$. 18. $\frac{d^2y}{dx^2}=2x\frac{dy}{dx}+3$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 19. The C.F. of the equation $\frac{d^2y}{dx^2}+\frac{3dy}{dx}+2y=e^{-x}$ A) $c_1e^{-x}+c_2e^{-2x}$. B) $c_1e^x+c_2e^{2x}$. C) $c_1e^{-2x}+c_2e^{-2x}$. D) $c_1e^{3x}+c_2e^{2x}$. Show Answer Correct Answer: A) $c_1e^{-x}+c_2e^{-2x}$. 20. $y=e^{\left(4x+5\right)}-7$ $y$ A) $y>-7$. B) $y<-7$. C) $y<7$. D) $y>7$. E) $-7 Show Answer Correct Answer: A) $y>-7$. 21. Differential equation of the curve y=Acosx-Bsinx, where A and B are arbitrary constant is A) Y$^{" }$+xy=0. B) Y$^{"}$-y=0. C) Y$^{"}$+y=0. D) Y$^{"}$+x=0. Show Answer Correct Answer: C) Y$^{"}$+y=0. 22. How many degrees is/are this DE? (y" ')$^{3}$ + 3y" + 6y'-12 = 0 A) 2. B) 1. C) 3. D) 4. Show Answer Correct Answer: C) 3. 23. Explain the concept of time in CPS modeling. A) Time in CPS modeling is irrelevant to system performance. B) Time in CPS modeling is a dimension that influences the behavior and interactions of physical and computational components, represented as discrete or continuous time. C) Time in CPS modeling is always represented as a fixed value. D) Time is only considered in computational components, not physical ones. Show Answer Correct Answer: B) Time in CPS modeling is a dimension that influences the behavior and interactions of physical and computational components, represented as discrete or continuous time. 24. The Fourier Sine Transform of $e^{-ax}$ A) $F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\\frac{a}{a^2+s^2}$. B) $F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\\frac{s}{a^2+s^2}$. C) $F_c\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\\frac{s}{a^2+s^2}$. D) None of the above. Show Answer Correct Answer: B) $F_s\left[e^{-ax}\right]=\sqrt{\frac{2}{\pi}}\\frac{s}{a^2+s^2}$. 25. Mdx +Ndy = 0 is exact iff A) $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$. B) $\frac{\partial M}{\partial y}=-\frac{\partial N}{\partial x}$. C) $\frac{\partial M}{\partial x}=\frac{\partial N}{\partial y}$. D) $\frac{\partial M}{\partial x}=-\frac{\partial N}{\partial y}$. Show Answer Correct Answer: A) $\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$. ← 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 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books