Download OU B.Sc Computer Science 2nd Sem Differential Equations Important Questions

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Subject Title: Differential Equations

Year: |

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Semester: 1l

Unit - |: Differential Equations of first order and first degree

1. Solve : xdx + ydy = 0
2. Solve : dy/dx = (2x+1)/(y+1)
3. Solve : dy/dx = (y/(x²+x+1))

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4. Solve : (x² + y²)dy = 2xydx
5. Solve : (1+e^x/y)dx + e^x/y[1-(x/y)]dy = 0
6. Solve : (x+y-1)dy = (x+y+1)dx
7. Solve : (1-x²)dy/dx - x + 2xy = xv(1-x²)
8. Solve : dy/dx = (x+y+1)²

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9. Show that the necessary and sufficient condition for the differential equation Mdx+Ndy=0 to be exact is that ?M/?y = ?N/?x
10. Solve : y sin2xdx-(1+y² + cos 2x)dy=0
11. If the differential equation Mdx+Ndy=0 is homogeneous and Mx+Ny?0, then show that 1/(Mx+Ny) is the integrating factor .Solve x²ydx-(x³ + y³)dy=0
12. Find the general solution of v(1-x²)dy + v(1-y²)dx=0
13. Solve the differential equation (e^x+1)ydy+(y+1)dx=0

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14. Solve: (3x²y³e^x +y³ + y²)dx+(x³y²e^x - xy)dy=0
15. Solve (y² + 2x²y)dx + (2x³ - xy)dy=0
16. Solve (xy² -x²)dx + (3x²y² + x²y - 2x³ + y²)dy=0
17. Solve xdx+ydy=a² [xdy-ydx]/(x²+y²)
18. Solve (yz+2x)dx+(zx-2z)dy+(xy-2y)dz=0

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19. Solve :(y² + yz)dx + (z² + zx)dy + (y² - xy)dz = 0
20. Solve dx/(y²z) = dy/(x²z) = dz/(x²y²)

UNIT-2

Differential Equations of first order but not of first degree and applications of first order differential equations

23. Solve x²p² + xyp -6y² =0

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24. Solve p=log(px-y)
25. The charcoal from a tree killed in the volcanic eruption that formed a lake contained 44.5% of ¹⁴C, found in living matter .About how old is the lake (half life of ¹⁴C, is 5600 approximately).
26. Find the Orthogonal trajectories for y=c₁e^2x
27. Solve (p-xy)(p-x²)(p-y²)=0
28. Solve p²+2py cotx=y².

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29. Solve (p+y+x)(xp+y+x)(p+2x)=0
30. Solve p³(x+2y)+3p²(x+y)+(y+2x)p=0
31. Solve y=xp² + x⁴p⁵ (or) Solve y+pX=x⁴p⁵ [p=dy/dx]
32. Solve y=2px+tan^-1(xp²) where p=dy/dx
33. Solve y=yp²+2px.

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34. Reduce (y-px)(p-1)=p to clairaut’s form and find the solution.
35. Solve sin px cosy=cos px siny +p where p=dy/dx
36. Solve y=2px+y²p³.
37. The bacteria in a colony can grow unchecked/by the law of exponential growth y=y₀e^kt.The colony starts with one bacterium and doubles every half hour. How many bacteria will the colony contain-at the end of 24 hours .
38. If 100 mg of radium is reduced to 90 mg of a radium in 200 years.Determine how much radium will remain-.at the end of 1000 years.Also find the half life of radium.

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39. It is found that 0.5 percent of radium disappears in 12 years. (a)What percentage will disappear in 1000 years (b) What is the half life of radium?
40. If Rs.10,000 is invested at 6% per annum,find what amount has accumulated after 6 years if interest is compounded (a)Annually (b)Quarterly (c)Continuously.
41. Find the family orthogonal to the family y=ce^mx of exponential curves.Determine the members of each family passing through (0,4).
42. Find the orthogonal trajectory of r=c₁(1-sin?).

Prepared by: Afreen Begum

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Updated on: 13-02-2020

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