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Class 12 Mathematics: Differential Equations
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MCQs on differential equations basics, general and particular solutions, first order and first degree differential equations methods, differential equation formation, linear first and second order differential equations.

Class 12 Mathematics: Differential Equations
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25 Questions

1. What will be the required solution of d2y/dx2 – 3dy/dx + 4y = 0?
2. What is the solution of dy/dx = (6x + 9y – 7)/(2x + 3y – 6)?
3. If y = t(x) be a differentiable function ᵾ x € R, then which of the following is always true?
4. Which of the following functions is a solution for the differential equation xy’-y=0?
5. What is the solution of the equation(y + x(√xy)(x + y))dx – (y + y(√xy)(x + y))dy = 0?
6. Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{2+x^3}{4-y^3}\).
7. Find the order and degree of the differential equation 7y’-3y=0.
8. Find the general solution of the differential solution \(\frac{dy}{dx}=2-x+x^3\).
9. What will be the general solution of differential equation for 2x – y dx + 2y – x dy = 0?
10. What is thedifferential equation whose solution represents the family y = ae3x + bex?
11. A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the distance from the origin at the end of 4 seconds?
12. Find the general solution of the differential equation \(\frac{dy}{dx}=\frac{3 \,sec\,⁡y}{2 \,cosec⁡\,x}\).
13. Find the order and degree of the differential equation 3y”-y’-ey=0
14. What is the differential equation whose solution represents the family c(y + c)2 = x3?
15. Which one of the following is correct if we differentiate the equation xy = aex + be-x two times?
16. Find the particular solution for the differential equation \(\frac{dy}{dx}=\frac{3x^2}{7y}\) given that, y=1 when x=1.
17. What will be the value of dy/dx = (x + 2y + 3)/(2x + 3y + 4)?
18. Which of the following functions is the solution of the differential equation \(\frac{dy}{dx}\)+2y=0?
19. The function y=3 cos⁡x is a solution of the function \(\frac{d^2 y}{dx^2}-3\frac{dy}{dx}\)=0.
20. What is the differential equation of all parabolas whose directrices are parallel to the x-axis?
21. A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. What is the equation of such curve passing through (0, k)?
22. A normal is drawn at a point P(x, y) of a curve. It meets the x-axis at Q. If PQ is of constant
length k. Then what is the differential equation describing such curve?
23. If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x?
24. Which of the following differential equations given below has the solution y=log⁡x?
25. Which of the following functions is a solution for the differential equation \(\frac{dy}{dx}\)-14x=0?

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