Important Questions for CBSE Class 12 Maths Chapter 9 - Differential Equations


CBSE Class 12 Maths Chapter-9 Important Questions – Free PDF Download

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CBSE Class 12 Mathematics Important Questions Chapter 9 – Differential Equations


1 Mark Questions

1. Find the order and degree. +y2+=0
Ans. order =3
Degree = not define.


2. Verify that the functions is a sol of the corresponding diff. req. 
Ans. 




Hence prove.


3.Form the differential equation of the family of hyper bolas having foci On x-axis and center at origin.
Ans. 








4. Find the order and degree
Ans. order = 2
degree = 1


5. Verify that the function is a solution of the corresponding diff eq.

Ans. 



proved.


6. Find order and degree. 
Ans. order = 3
degree = not define


7. Verify that the function is a solution of the corresponding diff eq.

Ans. 




8. Find order and degree. 
Ans. order = 4
degree = not define


9. Verify that the function is a solution of the corresponding diff eq. 
Ans. 
Proved


10. Write the order and degree of the diff equation 
Ans. 



11. Verify that the given functions is a solution of the corresponding diff eq. 
Ans. y = Cos x + c




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4 Mark Questions

1. Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
Ans. 






2. Solve the diff. equ. sec2x.tan y dx + sec2 y tan x dy = 0
Ans. Sec2x. tan y dx = -sec2y tan x dy


3. Solve the diff eq. y log y dx –x dy = 0
Ans. 





4. Solve x cos 
Ans. 





0


5. Solve
Ans. 








6. Form the differential equation representing the family of ellipses having foci on x – axis and centre at the origin.
Ans. 

diff eq (i) w. r. t. x



diff w. r. t. x


7. Form the diff. eq of the family of circles touching the x – axis at origin.
Ans. Let (o, a) be
The coordinate of circle.





Put a and y – a in eq (1)




8. Solve the diff eq. 
Ans. 




9. Solve Cos 
Ans. 




10. Solve. 
Ans. 









11. Solve 
Ans.














12. Form the differential equation representing the family of curves given by (x-a)2 + 2y= a2, where a is an arbitrary constant.
Ans. 
diff both side w.r.t.x




13. Form the diff. equation of the family of circles in the second quadrant and touching the coordinate axes.

Ans. Eq. of circle is





14. Solve the diff eq. 
Ans. 







15. Solve 
Ans. 






16. Solve 
Ans. 











17. Solve 
Ans. 














18. Form a differential equation representing the given family of curve by eliminating arbitrary constants a and b. 
Ans. 






19. Form a differential equation representing the given family of curve by eliminating arbitrary constants a and b. Y = ex (a Cos x + b Sin x)
Ans. 






20. Solve the diff eq. 
Ans. 


21. Find the equation of the curve passing through the point whose diff eq. is Sin x Cos y dx + Cos x . Sin y dy = 0
Ans. Sin x. Cos y dx = – Cos x. Sin y dy






22. Solve 
Ans. 






23. Solve the diff eq. 
Ans. 









24. Form a differential equation representing the given family of curve by elimination arbitrary Constants a and b. 
Ans. 





25. Form a differential equation representing the given family of curve by elimination arbitrary Constants a and b. 
Ans. 




26. Find the particular Solution of the diff. equation 
Ans. 




27. Solve the diff. eq 
Ans. 










28. Solve the diff. eq 
Ans. 

Let y = v x















29. Solve the following diff eq. 
Ans. 











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6 Marks Questions

1. Find the general sol. of the diff eq.
Ans. 














2. Find the particular sol of the diff. eq. Given that y = 0 when x = 
Ans.











3. Find the particulars solution of diff . equation.