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Engineering Math Practice Test: Ordinary Differential Equations - First Order & First Degree
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Ordinary Differential Equations - First Order & First Degreetopics include:  First order first degree differential equations, homogeneous form, seperable and homogeneous equations, bernoulli equations, clairauts and lagrange equations, orthogonal trajectories, natural growth and decay laws, newtons law of cooling and escape velocity, simple electrical networks solution, mathematical modeling basics, geometrical applications, first order linear and nonlinear differential equations. An ordinary differential equation (ODE) is a differential equation that depends on a single independent... Show more
Engineering Math Practice Test: Ordinary Differential Equations - First Order & First Degree
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25 Questions

1. What is the derivative of z=3x*logx+5x6 with respect to x?
2. Which of the following is not an example of linear differential equation?
3. Obtain the general solution for the equation xp2+px-py+1-y=0 where p=\(\frac{dy}{dx}\).
4. In recurrence relation, each further term of a sequence or array is defined as a function of its succeeding terms.
5. A racer accelerates from a stop so that its speed is 10t m/s t second after starting how far will the car go in 4 seconds?
6. Solution of the differential equation sec2 x tan⁡y dx + sec2 y tan⁡x dy=0 is _______
7. Solution of the differential equation \(\frac{dy}{dx} = \frac{x+2y-3}{2x+y-3}\) is _____
8. Solution of the differential equation \(\frac{dy}{dx} + \frac{y}{x} = y^2\) x is ________
9. Singular solution for the Clairaut’s equation \(y = y’x+\frac{a}{y’}\) is given by _______
10. Solution of the differential equation \(\Big[\frac{e^{-2\sqrt{x}}}{\sqrt{x}} – \frac{y}{\sqrt{x}}\Big] \frac{dy}{dx} = 1, \,x≠0\) is _______
11. Solution of the differential equation \(xy \frac{dy}{dx} = 1+x+y+xy\) is ______
12. Solution of the differential equation \(\frac{dy}{dx} -y \,tan⁡x = \frac{sin⁡x cos^2⁡x}{y^2}\) is ______
13. Solution of the differential equation \(\frac{dy}{dx} = \frac{y(x-y ln⁡y)}{x(x ln x-y)}\) is _____________
14. Find the general solution of the D.E y = 2xy’ – 3(y’)2.
15. Which of the following correctly defines ordinary differential equations?
16. For the differential equation \(\frac{dy}{dx}\) – 3y cot⁡x = sin⁡2x; y=2 when x=\(\frac{\pi}{2}\), its particular solution is ______
17. Solution of the differential equation (x-y)dy=(x+y+1)dx is _____
18. What is the slope of the equation, y= x2+8?
19. Solution of the differential equation (3y-7x+7)dx+(7y-3x+3)dy=0 is ______
20. A rectangular frame is to be made of 240 cm long. Determine the value of the length of the rectangle required to maximize the area.
21. Solve the differential equation \(\frac{dy}{dx} = \frac{x^2+y^2}{3xy}\) is _______
22. Solution of the differential equation 6y2 dx – x(x3 + 2y)dy = 0 is ________
23. Find the solution for \(\lim_{x\to 0}⁡ \frac{ax}{ax+x}.\)
24. In the formation of differential equation by elimination of arbitrary constants, after differentiating the equation with respect to independent variable, the arbitrary constant gets eliminated.
25. What is the differential equation of a family of parabolas with the foci at the origin and axis along the X-axis?