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Maths Book back answers and solution for Exercise questions - Mathematics : Ordinary Differential Equations: Formation of Differential Equations from Geometrical Problems - Exercise Problem Questions with Answer, Solution

**EXERCISE 10.3**

**1. Find the differential equation of the family of (i) all non-vertical lines in a plane (ii) all non-horizontal lines in a plane.**

**2. Form the differential equation of all straight lines touching the circle x2 + y2 = r2.**

**3. Find the differential equation of the family of circles passing through the origin and having their centres on the x -axis.**

**4. Find the differential equation of the family of all the parabolas with latus rectum 4 a and whose axes are parallel to the x -axis.**

**5. Find the differential equation of the family of parabolas with vertex at (0, −1) and having axis along the y -axis.**

**6. Find the differential equations of the family of all the ellipses having foci on the y -axis and centre at the origin.**

**7. Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be−8x , where A and B are arbitrary constants.**

**8. Find the differential equation of the curve represented by xy = ae x + be − x + x2.**

**Answers:**

**3. x2 + 2xy dy/dx − y2 = 0**

**4. 2 ay ′′ + y′3 = 0**

**5. xy′ − 2y − 2 = 0**

**6. xy ′ 2 + xyy′′ − yy′ = 0**

**7. d2y/dx = 64 y**

**8. xy′′ + 2 y ′ + x2 − xy − 2 = 0**

Tags : Problem Questions with Answer, Solution , 12th Maths : UNIT 10 : Ordinary Differential Equations

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12th Maths : UNIT 10 : Ordinary Differential Equations : Exercise 10.3: Formation of Differential Equations from Geometrical Problems | Problem Questions with Answer, Solution

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