SATHEE: Differential Equations 1 Question 7

Differential Equations 1 Question 7

7. The differential equation $\frac{d y}{d x} = \frac{\sqrt{1 - y^{2}}}{y}$ determines a family of circles with

(2007, 3M)

(a) variable radii and a fixed centre at $(0, 1)$

(b) variable radii and a fixed centre at $(0, - 1)$

(d) fixed radius 1 and variable centres along the $Y$ -axis

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Answer:

Correct Answer: 7. (c)

Solution:

Given, $\frac{d y}{d x} = \frac{\sqrt{1 - y^{2}}}{y}$

$\begin{array}{ll} \Rightarrow & \int \frac{y}{\sqrt{1 - y^{2}}} d y = \int d x \\ \Rightarrow & - \sqrt{1 - y^{2}} = x + c \Rightarrow (x + c)^{2} + y^{2} = 1 \end{array}$

Here, centre $(- c, 0)$ and radius $= 1$

Differential Equations 1 Question 7

7. The differential equation $\frac{d y}{d x} = \frac{\sqrt{1 - y^{2}}}{y}$ determines a family of circles with

Answer:

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Differential Equations 1 Question 7

7. The differential equation dydx=1−y2y determines a family of circles with

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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7. The differential equation $\frac{d y}{d x} = \frac{\sqrt{1 - y^{2}}}{y}$ determines a family of circles with