Ordinary Differential Equations Mcqs with Answers

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21. The differential equation with solution y = A sin x + B cos x is:
A. \frac{dy}{dx}+y=0
B. \frac{dy}{dx}-y=0
C. \frac{d^2y}{dx^2}+y=0
D. \frac{d^2y}{dx^2}-y=0
22. The differential equation of all parabolas whose axis is parallel to the y-axis is:
A. \frac{dy}{dx}=x^2+b
B. \frac{d^2y}{dx^2}=2x
C. \frac{d^3y}{dx^3}=0
D. All of these
23. A function f : R ²  → R is called ____________ of degree n if
f(tx, ty) = t^nf(x, y), where t is a nonzero real number.
A. Linear
B. Exact
C. Homogeneous
D. Separable
24. Which of the following is homogeneous?
A. \sqrt{xy}
B. cos(\frac{y}{x})
C. ln(e^{xy})
D. All of these
25. The degree homogeneous function \frac{x^{10}+y^{10}}{x^2+y^2}  is
A. 7
B. 9
C. 8
D. 2




26. A homogeneous equation  can be transformed into a separable equation by substitution.
A. y = vx²
B. y = vx
C. y = x²
D. y = x
27.  \frac{dy}{dx}= g(\frac{y}{x})  is homogeneous, its separable form is
A. [v – g(v)]dx + dv = 0
B. [v – g(v)]dx + xdv = 0
C. [x – g(x)]dx + dv = 0
D. [x – g(x)]dx + vdv = 0
28. The differential equation (a_1x + b_1y + c_1)dx + (a_2x + b_2y + c_2) = 0 is:
A. Exact
B. Not exact
C. Homogeneous
D. Non linear
29. By substitution____________________differential equation (a_1x + b_1y + c_1)dx + (a_2x + b_2y + c_2) = 0 will
be reduced to homogeneous equation.
A. x = X + h, y = Y + k
B. x = X – h, y = Y – k
C. z = a_1x + b_1y
D. None of these
30. The differential equation (a_1x + b_1y + c_1)dx + (a_2x + b_2y + c_2) = 0 is not exact, but if \frac{a_1}{a_2} \neq \frac{b_1}{b_2} then the substitution … will work to reduce it to homogeneous form?
A. x = X + h, y = Y + k
B. x = X – h, y = Y – k
C. z = a_1x + b_1y
D. None of these




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