Ordinary Differential Equations Mcqs with Answers

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Vector and tensor analysis mcqs with answers

11. The graph of a particular solution (integral) is called … of the differential equation.
A. Locus
B. Differential curve
C. Integral curve
D. All of these
12. A solution of the differential equation \fn_jvn (\frac{dy}{dx})^2-x\frac{dy}{dx}+y=0 is:
A. y = 2
B. y = 2x
C. y = 2x – 4
D. y = 2x + 4
13. Solution of the differential equation \fn_jvn \frac{dy}{dx}= 2x subject to the condition y(1)= 4 is:
A. y = x²
B. y = x + 3
C. y = x² + 3
D. y = 2x³
14. If y = A sin x + B cos x , then what is y(0)
A. 0
B. 1
C. A
D. B
15. The differential equation \fn_jvn x^2dy+y^2dx=0 has order
A. 1
B. 2
C. 3
D. 4




16. A differential equation F(x)G(y)dx + f(x)g(y)dy = 0 is called _____________if it can be written as  \fn_jvn \frac{F(x)}{f(x)}dy+\frac{g(x)}{G(x)}dx=0
A. Separable
B. Exact
C. Homogeneous
D. Linear

17. \fn_jvn \frac{dy}{dx}=\frac{y^2}{x}  has solution.
A. y ² + x ² = c
B. 3y = 2x ² + c
C. 3y² = 2x³ + c
D. 3y² = x + c
18. \fn_jvn \frac{dy}{dx}=\frac{1}{xtany}  has solution
A. x cos y = \fn_jvn e^c
B. x sin y = \fn_jvn e^c
C. x sin y = c
D. None of these
19. \fn_jvn \frac{dy}{dx}=-y^2sinx has solution
A. y + cos x = c
B. y + sin x = c
C. \frac{1}{y} + cos x = c
D. \frac{1}{y} + sin x = c

20. The differential equation (1 + x)dy – ydx = 0 has the general solution
A. y = c(1 + x)
B. y = c + x
C. y = cx
D. y = c + cx




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