Mathematics-II Tutorial Questions PDF
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Mr. ALIFER
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This document contains tutorial questions related to Mathematics-II. The questions cover topics such as differential equations, calculus, and related concepts. This is a guide for students to practice their skills.
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ADDITIONAL TUTORIAL QUESTIONS Mathematics-II Course Code: 24MAT-142 Branch:...
ADDITIONAL TUTORIAL QUESTIONS Mathematics-II Course Code: 24MAT-142 Branch: Semester-II Faculty: Mr. ALIFER Civil/ME/ECE/EEE/CSE UNIT-1 π/π π ππ π π 1. Find the order and degree of the ODE (π ππ ) = π + π (π π). π π π π π π π π 2. Find the order and degree of the ODE π ππ + (π π) = πππ (π π). 3. Find the DE of the curve: π = π πππ β π πβππ , πππππ π πππ π πππ ππππππππππ. 4. Find the DE of the curve: π = ππππππ + ππππππ, πππππ π πππ π πππ ππππππππππ. 5. Find the DE representing all the circles of radius βπβ in the π-π plane. 6. Solve: ππππ π ππππ π π + ππππ π ππππ π π = π. π π 7. Solve: π π = ππβπ + ππ πβπ. π π ππβπβπ 8. Solve: π π = ππβππ+π. π π 9. If π is the function of π, such that the differential coefficient is equal to πππ (π + π) + π π πππ (π + π). Find out a relation between π and π, which is free from any derivative/differential. 10. Solve: (ππ β πππ ) π π + πππ π π = π. 11. Solve: (ππ + ππ ) π π β πππ π π = π. π π 12. Solve: π πππ ( ) (ππ π + ππ π) = π πππ ( ) (ππ π β ππ π). π π π π 13. Solve: π β π = π β(ππ + ππ ). π π π π 14. Solve: (π + ππ ) π π + πππ = πππ. 15. Solve: (π + πππ )π π = ππ π. π π 16. Solve: (π + π + π) = π. π π π π π 17. Solve: π π + π ππππ = π πππππ. π π π βπ π 18. Solve: π π = π+ππ (ππππ β π). βπ π π π 19. Solve: (π + ππ ) + (π β πβπππ ) π π = π. π π 20. Solve: π π = ππ ππ β ππ. π π 21. Solve: = ππβπ (ππ β ππ ). π π π π 22. Solve: π π π + π ππππ = ππ ππ. 23. Solve: (ππ + π) ππππ π π + ππ ππππ π π = π. 24. Solve: ππ π π π β (ππ + ππ )π π = π. 25. Solve: (ππππ + ππ + π)π π π + (ππ ππ β ππ + π)π π π = π. π π π π π 26. Solve: βπ + ππ = π. π ππ π π π π π 27. Solve: β ππ = π. π ππ π π π π π 28. Solve: π ππ + π π + π = ππ. π π π π π 29. Solve: π ππ + π π π + ππ = πππ. π π π π π 30. Solve: π ππ + π π β ππ = πππ. 31. Solve: (π«π + ππ«π + ππ« + π)π = πβπ. π π π π π 32. Solve: βπ + ππ = πππππ. π ππ π π 33. Solve: (π«π π + π« β π« β π)π = πππ ππ. 34. Solve: (π«π + π)π = πππ ππ. 35. Solve: (π«π + π)π = πππ ππ. 36. Solve: (π«π + π)π = πππππ. ππππ. 37. Solve: (π«π + ππ« + π)π = ππ. 38. Find the general solution of the equation πβ²β²β² β πβ²β² = ππππ + ππ. π π π 39. Solve: + ππ = ππππ π. π ππ π π π π π 40. Solve: π ππ β π π π β ππ = ππ + ππ + πππ ππ. 41. Solve: π β π = ππ πππ. β²β² 42. Solve: (π«π β ππ« + π)π = πππ ππππ. 43. Solve: (π«π β ππ« + π)π = ππ πππ. 44. Solve: (π«π + π)π = π ππππ. 45. Solve: (π«π + π)π = πππππ ππππ. 46. Solve the initial value problem π π π + π = ππβππ ππππ, π(π) = π, πβ² (π) = π. π ππ π π π π π 47. Solve: π ππ β π π π + ππ = πππ πππ πππππ. π π π π π π π 48. Solve: βπ + π = π ππ ππππ with π(π) = π and ( ) = π. π ππ π π π π π=π 49. Solve: (π«π β ππ« + π)π = πππ πππ πππππ. 50. Solve: (π«π + ππ )π = πππ ππ
