Which of the following differential equations has y = c 1 e x + c 2 e –x as the general solution?

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 9. Differential Equations

Subject: Maths - Class 12^th

Q. No. 11 of Exercise 9.3

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11

Which of the following differential equations has y = c₁e^x + c₂e^–x as the general solution?

It is given that y = c₁e^x + c₂e^-x

Now, differentiating both sides w.r.t. x, we get,

Again, differentiating both sides w.r.t. x, we get,

Therefore, the required differential equation is .

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Chapter Exercises

Exercise 9.1

Exercise 9.2

Exercise 9.3

Exercise 9.4

Exercise 9.5

Exercise 9.6

Miscellaneous Exercise

1

In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

2

In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y² = a(b² – x²)

3

In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = a e^3x + b e^–2x

4

In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e^2x (a + bx)

5

In each of the question, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.
y = e^x (a cos x + b sin x)

6

Form the differential equation of the family of circles touching the y-axis at origin.

7

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

8

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

9

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

10

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

11

Which of the following differential equations has y = c₁e^x + c₂e^–x as the general solution?

12

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