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

Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 9 – Differential Equations prepared by expert Maths teachers from latest edition of CBSE(NCERT) books, On CoolGyan.Org to score more marks in CBSE board examination.

You can also Download __Maths Revision Notes Class 12__ to help you to revise complete Syllabus and score more marks in your examinations.

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**CBSE Class 12 Mathematics Important Questions Chapter 9 – Differential Equations**

**1 Mark Questions**

**1. Find the order and degree. +y ^{2}+=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. sec ^{2}x.tan y dx + sec^{2} y tan x dy = 0**

**Ans.**Sec

^{2}x. tan y dx = -sec

^{2}y 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^{2 }= a^{2}, 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 = e ^{x} (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. **