In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3 pdf, free NCERT solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3 book pdf download.

Board | CBSE |

Textbook | NCERT |

Class | Class 12 |

Subject | Maths |

Chapter | Chapter 9 |

Chapter Name | Differential Equations |

Exercise | Ex 9.3 |

Number of Questions Solved | 12 |

Category | NCERT Solutions |

## NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations Ex 9.3

**In each of the following, Q. 1 to 5 form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.**

**Ex 9.3 Class 12 Maths Question 1.****Solution:**

Given that …(i)

differentiating (i) w.r.t x, we get

…(ii)

again differentiating w.r.t x, we get

which is the required differential equation

**Ex 9.3 Class 12 Maths Question 2.**

y² = a(b² – x²)**Solution:**

given that

y² = a(b² – x²)…(i)

**Ex 9.3 Class 12 Maths Question 3.**

y = ae^{3x}+be^{-2x}**Solution:**

Given that

y = ae^{3x}+be^{-2x} …(i)

**Ex 9.3 Class 12 Maths Question 4.**

y = e^{2x} (a+bx)**Solution:**

y = e^{2x} (a+bx)

**Ex 9.3 Class 12 Maths Question 5.**

y = e^{x}(a cosx+b sinx)**Solution:**

The curve y = e^{x}(a cosx+b sinx) …(i)

differentiating w.r.t x

**Ex 9.3 Class 12 Maths Question 6.**

Form the differential equation of the family of circles touching the y axis at origin**Solution:**

The equation of the circle with centre (a, 0) and radius a, which touches y- axis at origin

**Ex 9.3 Class 12 Maths Question 7.**

Form the differential equation of the family of parabolas having vertex at origin and axis along positive y-axis.**Solution:**

The equation of parabola having vertex at the origin and axis along positive y-axis is

**Ex 9.3 Class 12 Maths Question 8.**

Form the differential equation of family of ellipses having foci on y-axis and centre at origin.**Solution:**

The equation of family ellipses having foci at y- axis is

**Ex 9.3 Class 12 Maths Question 9.**

Form the differential equation of the family of hyperbolas having foci on x-axis and centre at the origin.**Solution:**

Equation of the hyperbola is

Differentiating both sides w.r.t x

which is the req. differential eq. of the hyperbola.

**Ex 9.3 Class 12 Maths Question 10.**

Form the differential equation of the family of circles having centre on y-axis and radius 3 units**Solution:**

Let centre be (0, a) and r = 3

Equation of circle is

x² + (y – a)² = 9 …(i)

Differentiating both sides, we get

which is required equation

**Ex 9.3 Class 12 Maths Question 11.**

Which of the following differential equation has as the general solution ?

(a)

(b)

(c)

(d) **Solution:**

(b)

**Ex 9.3 Class 12 Maths Question 12.**

Which of the following differential equations has y = x as one of its particular solution ?

(a)

(b)

(c)

(d) **Solution:**

(c) y = x

**All Chapter NCERT Solutions For Class12 Maths**

—————————————————————————–**All Subject NCERT Solutions For Class12**

***************************************************Remark:**

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share Careerkundali.in to your friends.

**Best of Luck!!**