This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 28 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 28 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Part C. Find the equation (inverse method) from the general solution:20. y = $C_{1}e^{7x} + C_{2}e^{-3x}$ A) Y" -4y'-21y = 0. B) Y" + 4y'-21y = 0. C) Y" -10y' + 21y = 0. D) Y" + 10y' + 21y = 0. Show Answer Correct Answer: A) Y" -4y'-21y = 0. 2. Find the area between the curves \( y = x^2 \) and \( y = x \) from \( x = 0 \) to \( x = 1 \). A) 0.25. B) 0.1667. C) 0.5. D) 0.1. Show Answer Correct Answer: B) 0.1667. 3. $ydx-\left(x-2\right)dy=0$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: B) Separable. 4. If $\frac{dy}{dx}=3e^{2x}, $ $x=0, \\y=\frac{5}{2}, $ A) $\frac{3}{2}e^{2x}+1$. B) $\frac{3}{2}e^{2x}+5$. C) $\frac{3}{2}e^{2x}+\frac{1}{2}$. D) $3e^{2x}+2$. Show Answer Correct Answer: A) $\frac{3}{2}e^{2x}+1$. 5. Find the specific solution to the following homogeneous DE, given that x = 0 when y = 1:$3\frac{d^2y}{dx^2}+4y=0$ A) $y=\cos((\frac{2\sqrt{3}}{3})x)$. B) $y=\cos((\frac{2\sqrt{3}}{3})x)+\sin((\frac{2\sqrt{3}}{3})x)$. C) $y=e^{-\frac{4x}{3}}$. D) $y=Ae^{-\frac{4x}{3}}$. Show Answer Correct Answer: A) $y=\cos((\frac{2\sqrt{3}}{3})x)$. 6. Find the particular solution to the differential equation $\frac{dy}{dx}=\frac{2x^3}{y^2}$ $\left(2, 3\right)$ A) $y=\ln\left(e^x+3\right)$. B) $y=\left(\frac{3x^4}{4}+3\right)^{\frac{1}{3}}$. C) $y=\left(\frac{3x^4}{2}+1\right)^{\frac{1}{3}}$. D) $y=\left(\frac{3x^4}{2}+3\right)^{\frac{1}{3}}$. Show Answer Correct Answer: D) $y=\left(\frac{3x^4}{2}+3\right)^{\frac{1}{3}}$. 7. Name the main types of PDEs. A) Linear, Quadratic, Cubic. B) Discrete, Continuous, Mixed. C) Static, Dynamic, Stochastic. D) Elliptic, Parabolic, Hyperbolic. Show Answer Correct Answer: D) Elliptic, Parabolic, Hyperbolic. 8. What type of differential equation is dy/dx = x/y? A) Nonlinear differential equation. B) Exact differential equation. C) First-order homogeneous differential equation. D) Second-order linear differential equation. Show Answer Correct Answer: C) First-order homogeneous differential equation. 9. What is homogeneous A) Same degree. B) Same order. C) Different degree. D) Different order. Show Answer Correct Answer: A) Same degree. 10. If the acceleration function is $a(t) = 6t-4$ $v(t)$ $v(0) = 5$ A) $v(t) = 3t^2-4t + 5$. B) $v(t) = 3t^2-4t$. C) $v(t) = 3t^2 + 4t + 5$. D) $v(t) = 3t^2 + 4t$. Show Answer Correct Answer: A) $v(t) = 3t^2-4t + 5$. 11. Complementary function of $y" +4y'+13y=2e^{-x}$ A) $e^{2x}\left(c_1\cos3x+c_2\sin3x\right)$. B) $e^{-2x}\left(c_1\cos3x+c_2\sin3x\right)$. C) $e^{3x}\left(c_1\cos2x+c_2\sin2x\right)$. D) $\left(c_1\cos3x+c_2\sin3x\right)$. Show Answer Correct Answer: B) $e^{-2x}\left(c_1\cos3x+c_2\sin3x\right)$. 12. For f(x, y) = xy, the total differential df is: A) X dy + y dx. B) Dx + dy. C) X dx + y dy. D) Y dx + x dy. Show Answer Correct Answer: A) X dy + y dx. 13. Determine the general solution of the differential equation $\frac{dy}{dx} = 4y$ A) $y = Ce^{4x}$. B) $y = Ce^{2x}$. C) $y = Ce^{x}$. D) $y = Ce^{3x}$. Show Answer Correct Answer: A) $y = Ce^{4x}$. 14. Wronskian formula for second-order DE $y" +P(x)y'+Q(x)y=0$ A) $W(x)=Ce^{\int P(x)dx}$. B) $W(x)=Ce^{-\int P(x)dx}$. C) $W(x)=Ce^{\int Q(x)dx}$. D) $W(x)=Ce^{-\int Q(x)dx}$. Show Answer Correct Answer: B) $W(x)=Ce^{-\int P(x)dx}$. 15. Dy/dx = 3x-2y and y(0) = k. Starting with x = 0 and a step size of 1, find k if y(2) = 4.5 A) 1. B) 2. C) 1.5. D) 2.5. Show Answer Correct Answer: C) 1.5. 16. The auxiliary equation of the following ODE $D^2y-7Dy+6y=0$ A) $m^2-7m+6=0$. B) $m^2+7m-6=0$. C) $m^2-3m+5$. D) $\left(m^2-7m+6\right)y=0$. Show Answer Correct Answer: A) $m^2-7m+6=0$. 17. In the context of PDEs, what does the term "separation of variables" refer to? A) A method to solve PDEs by assuming a solution can be written as a product of functions, each depending on a single variable. B) A technique to classify PDEs based on their order. C) A way to derive boundary conditions for PDEs. D) A method to convert PDEs into ordinary differential equations. Show Answer Correct Answer: A) A method to solve PDEs by assuming a solution can be written as a product of functions, each depending on a single variable. 18. What is the difference between linear and nonlinear PDEs? A) Linear PDEs involve linear combinations of the unknown function and its derivatives, while nonlinear PDEs include nonlinear terms. B) Linear PDEs do not involve derivatives of the unknown function. C) Nonlinear PDEs cannot be solved using any numerical methods. D) Linear PDEs only have constant coefficients. Show Answer Correct Answer: A) Linear PDEs involve linear combinations of the unknown function and its derivatives, while nonlinear PDEs include nonlinear terms. 19. State the order of given Differential Equations $y^{\left(5\right)}$ A) 5. B) 1. C) 5 and 1. D) Zero. Show Answer Correct Answer: A) 5. 20. The equation y" +3y = sinx is: A) Linear and homogeneous. B) Linear and non-homogeneous. C) Non-linear. D) Exact. Show Answer Correct Answer: B) Linear and non-homogeneous. 21. Which of the following differential equation is a separable equation? A) $\left(x+x^2y\right)dy=\left(2x+xy^2\right)dx$. B) $\left(x+y\right)dx-2ydy=0$. C) $2ydx=\left(x^2+1\right)dy$. D) $y^2dx+\left(2x-3y\right)dy=0$. Show Answer Correct Answer: C) $2ydx=\left(x^2+1\right)dy$. 22. $x\left(\frac{\text{d}^2y}{\text{d}x^2}\right)+xy=1$ A) Second order differential equation. B) First order differential equation. C) First order differential equation at second degree. D) Second order differential equation at first degree. Show Answer Correct Answer: D) Second order differential equation at first degree. 23. By usual notations what is the general form of Lagrange's linear PDE. A) Pdx+qdy=0. B) Pp+Qq=R. C) Pdx+Qdy=Rdz. D) Non of the above. Show Answer Correct Answer: B) Pp+Qq=R. 24. $\frac{dy}{dx}+\frac{2x}{1-x^2}y-4x=0$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: A) Linear. 25. Find the general solution of the differential equation $e^{-y}\frac{\text{d}y}{\text{d}x}=\left(2-x^3\right)^2$ A) $-e^{-y}=\frac{-x^7}{7}+x^3-x+c$. B) $e^{-y}=\frac{x^7}{7}-4x^3-x+c$. C) $e^{-y}=\frac{-x^7}{7}+4x^4+4x+c$. D) $-e^{-y}=\frac{x^7}{7}-x^4+4x+c$. Show Answer Correct Answer: D) $-e^{-y}=\frac{x^7}{7}-x^4+4x+c$. ← 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