Let the solution curve of the differential equation xdy = <math> <mrow> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mi>y</mi> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>,</mo> <mtext> </mtext> <mtext> </mtext> <mi>x</mi> <mo>></mo> <mn>0</mn> </mrow> </math> <math><mrow><mrow><mrow><mroot><mrow><msup><mrow></mrow><mrow></mrow></msup><msup><mrow></mrow><mrow></mrow></msup></mrow></mroot></mrow></mrow></mrow></math> intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is:

x d y = ( x 2 + y 2 + y ) d x x d y − y d x x 2 = 1 + y 2 x 2 d x d ( y x ) 1 + ( y x ) 2 = d x x ⇒ l n ( y x + ( y x ) 2 + 1 ) = l n x + C α = 3 2

Let the solution curve of the differential equation xdy = <math> <mrow> <mrow> <mo>(</mo> <mrow> <mroot> <mrow> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mi>y</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow></mrow> </mroot> <mo>+</mo> <mi>y</mi> </mrow> <mo>)</mo> </mrow> <mi>d</mi> <mi>x</mi> <mo>,</mo> <mtext> </mtext> <mtext> </mtext> <mi>x</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math> <math><mrow><mrow><mrow><mroot><mrow><msup><mrow></mrow><mrow></mrow></msup><msup><mrow></mrow><mrow></mrow></msup></mrow></mroot></mrow></mrow></mrow></math>&nbsp;intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is:

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Maths Class 12th Differential Equations

Let the solution curve of the differential equation xdy = $(\sqrt[]{x^{2} + y^{2}} + y) d x, x > 0$ $^{}^{}$ intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is:

Option 1 -

$\frac{1}{2}$

Option 2 -

$\frac{3}{2}$

Option 3 -

$- \frac{3}{2}$

Option 4 -

$\frac{5}{2}$

3 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

$x d y = (\sqrt[]{x^{2} + y^{2}} + y) d x$

$\frac{x d y - y d x}{x^{2}} = \sqrt[]{1 + \frac{y^{2}}{x^{2}}} d x$

$\frac{d (\frac{y}{x})}{\sqrt[]{1 + {(\frac{y}{x})}^{2}}} = \frac{d x}{x} \Rightarrow l n (\frac{y}{x} + \sqrt[]{{(\frac{y}{x})}^{2} + 1}) = l n x + C$

$α = \frac{3}{2}$

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Let the solution curve of the differential equation xdy = $(\sqrt[]{x^{2} + y^{2}} + y) d x, x > 0$ $^{}^{}$ intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is:

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Let the solution curve of the differential equation xdy = ( x 2 + y 2 + y ) d x , x > 0 intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is:

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Let the solution curve of the differential equation xdy = $(\sqrt[]{x^{2} + y^{2}} + y) d x, x > 0$ $^{}^{}$ intersect the line x = 1 at y = 0 and the line x = 2 at y = . Then the value of is: