This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 12 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 12 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The eigenvalues of the coefficient matrix determine: A) The shape of the graph. B) The stability and type of solution. C) The particular integral. D) Nothing. Show Answer Correct Answer: B) The stability and type of solution. 2. At each point on a certain curve, the slope of the curve is $3x^2y$ A) $y=8e^{x^3}$. B) $y=x^3+8$. C) $y=e^{x^3}+7$. D) $y=\ln\left(x+1\right)+8$. Show Answer Correct Answer: A) $y=8e^{x^3}$. 3. $\frac{du}{dx}=cux$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 4. General solution of the equation $\left(x^3+3xy^2\right)dx+\left(3x^2y+y^3\right)dy=0$ A) $x^2+y^2=c$. B) $\frac{1}{12}\left(x^3+6xy^2+y^4\right)=c$. C) $\frac{1}{5}\left(8x^4+6x^3y+y^3\right)=c$. D) $\frac{1}{4}\left(x^4+6x^2y^2+y^4\right)=c$. Show Answer Correct Answer: D) $\frac{1}{4}\left(x^4+6x^2y^2+y^4\right)=c$. 5. Suppose you deposit $ 1000 in an account that pays 1.5% annual interest and it increases at a rate proportional to the present amount. How much money will you have after 7 years if the interest is compounded continuously? A) $ 1110.71. B) $ 7, 000. C) $ 10, 500. D) $ 36, 315, 502.67. Show Answer Correct Answer: A) $ 1110.71. 6. If R(x) is a decreasing function, then a Left Hand Riemann sum will be an ..... A) Underapproximation. B) Overapproximation. C) All the above. D) None of the above. Show Answer Correct Answer: B) Overapproximation. 7. The solution of linear differential equation $\frac{\text{d}y}{\text{d}x}+y=e^x$ A) $y=\frac{e^2+c}{4x^2}$. B) $y=\frac{ex^2}{4}+c$. C) $y=\frac{e^{4x}+c}{x^2}$. D) $y=\frac{e^x}{2}+Ce^{-x}$. Show Answer Correct Answer: D) $y=\frac{e^x}{2}+Ce^{-x}$. 8. What is the criterion for linear dependence in a set of functions? A) All functions must be zero. B) At least one function can be expressed as a linear combination of others. C) All functions must be independent. D) The Wronskian must be non-zero. Show Answer Correct Answer: B) At least one function can be expressed as a linear combination of others. 9. How would you CORRECTLY separate the following differential equation? $\frac{dy}{dx}=e^{\left(x+y\right)}$ A) $e^{-y}dy=e^xdx$. B) $-\frac{dy}{e^y}=e^xdx$. C) $\frac{dy}{e^{\left(x+y\right)}}=1dx$. D) $1dy=e^{\left(x+y\right)}dx$. Show Answer Correct Answer: A) $e^{-y}dy=e^xdx$. 10. The complementary function represents the solution of the: A) Homogeneous part. B) Non-homogeneous part. C) Singular equation. D) None. Show Answer Correct Answer: A) Homogeneous part. 11. If the roots of the auxiliary equation in an ODE are 1, -1, i, -i, then complementary function is y= ..... A) $Ae^x+Be^{-x}+C\cos x+D\sin x$. B) $Ae^x+Be^{-x}+C\cos x-D\sin x$. C) $Ae^x+xBe^{-x}+C\cos x+D\sin x$. D) $Ae^{ix}+Be^{-ix}+C\cos x+D\sin x$. Show Answer Correct Answer: A) $Ae^x+Be^{-x}+C\cos x+D\sin x$. 12. When an equation is solvable for y, it often gives: A) Explicit solution for y. B) A relation involving x. C) Multiple roots. D) None. Show Answer Correct Answer: A) Explicit solution for y. 13. 1/D stands for A) Particular Integral. B) Differentiation. C) Integration. D) Complementary Function. Show Answer Correct Answer: C) Integration. 14. Solve the non-homogeneous equation:y" + 9y = cos(3x). A) Y = C1 sin(3x) + C2 cos(3x)-(1/9) xsin(3x). B) Y = C1 cos(3x) + C2 sin(3x) +(1/6) xsin(3x). C) Y = C1 cos(3x) + C2 sin(3x)-(1/6) xcos(3x). D) Y = C1 cos(3x) + C2 sin(3x) + (1/9) x$^{2}$sin(3x). Show Answer Correct Answer: B) Y = C1 cos(3x) + C2 sin(3x) +(1/6) xsin(3x). 15. Which of the following represents a particular integral? A) The specific solution to the non-homogeneous part of a differential equation. B) The solution to the homogeneous part of a differential equation. C) The general solution to a differential equation. D) The derivative of the non-homogeneous part of a differential equation. Show Answer Correct Answer: A) The specific solution to the non-homogeneous part of a differential equation. 16. The singular solution is obtained by eliminating: A) P from equations. B) Y from equations. C) Xxx only. D) None. Show Answer Correct Answer: A) P from equations. 17. Find the general solution of the differential equation y'-ysin(x)=0. A) $|y|=Ce^{-\sin\left(x\right)}$. B) $|y|=Ce^{\sin\left(x\right)}$. C) $|y|=Ce^{-\cos\left(x\right)}$. D) $|y|=Ce^{\cos\left(x\right)}$. E) $|y|=-Ce^{\cos\left(x\right)}$. Show Answer Correct Answer: C) $|y|=Ce^{-\cos\left(x\right)}$. 18. The singular solution of Clairaut's equation is always: A) An envelope curve. B) Parallel lines. C) Polynomial. D) None. Show Answer Correct Answer: A) An envelope curve. 19. Integrating factor of $\cos^2x\\frac{dy}{dx}+y=\tan x$ A) $e^{\sec^2x}$. B) $e^{\tan x}$. C) $e^{\tan^2x}$. D) $e^{-\tan x}$. Show Answer Correct Answer: B) $e^{\tan x}$. 20. Given the de y'=2x+1 find y in terms of x for y(0)=1 A) X$^{2}$+x+c=y. B) Y=x$^{3}$+x+1. C) Y=x$^{2}$+x+1. D) Y=2x+1. Show Answer Correct Answer: C) Y=x$^{2}$+x+1. 21. For repeated roots, applying initial conditions helps to determine: A) Auxiliary roots. B) Arbitrary constants. C) Wronskian. D) Order of DE. Show Answer Correct Answer: B) Arbitrary constants. 22. $\frac{dt}{dx}=2x$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 23. Find the exact solution to the following equation given that y = 6, dy/dx =-5 when x = 0. $\frac{\text{d}^2y}{\text{d}x^2}+4\frac{\text{d}x}{\text{d}y}+5y=x^2+2x+4$ A) $y=e^{-2x}(2.72\cos x+0.36\sin x)+0.2x^2+0.08x+3.28$. B) $y=e^x(4.6\cos\left(-2x\right)+2.22\sin\left(-2x\right))+0.34x^2+0.8x+3.5$. C) $y=e^x(4.6-2.4x)+0.5x^2+3.14$. D) $y=e^{-2x}(2.14+0.86x)+1.2x^2+0.56x$. Show Answer Correct Answer: A) $y=e^{-2x}(2.72\cos x+0.36\sin x)+0.2x^2+0.08x+3.28$. 24. Bagaimana solusi berubah jika akar dari persamaan karakteristik adalah kompleks? A) Solusi menjadi nilai konstan. B) Solusi mencakup istilah osilasi yang melibatkan fungsi sinus dan kosinus. C) Solusi tidak memiliki akar real. D) Solusi disederhanakan menjadi persamaan linier. Show Answer Correct Answer: B) Solusi mencakup istilah osilasi yang melibatkan fungsi sinus dan kosinus. 25. The method of variation of parameters is preferred when: A) The complementary function is unknown. B) The non-homogeneous term is complex. C) Initial conditions are not given. D) The equation is of first order. Show Answer Correct Answer: B) The non-homogeneous term is complex. ← 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