<p>In column I differential equations are given in column II their solutions are given then match them</p> <table border="1" cellpadding="1" cellspacing="1" style="width:350px"> <tbody> <tr> <td style="text-align:center"> </td> <td style="text-align:center"><strong>Column I</strong></td> <td style="text-align:center"> </td> <td style="text-align:center"><strong>Column II</strong></td> </tr> <tr> <td>A)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mfrac><mrow><mi>d</mi><mi>y</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>+</mo><mi>x</mi><mo>=</mo><mn>0</mn></math></td> <td>p)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi></math></td> </tr> <tr> <td>B)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mfrac><mrow><mi>d</mi><mi>y</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>+</mo><mi>y</mi><mo>=</mo><mn>0</mn></math></td> <td>q)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mi>c</mi></math></td> </tr> <tr> <td>C)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>y</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mo>=</mo><mi>x</mi></math></td> <td>r)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mi>y</mi><mo>=</mo><mi>c</mi></math></td> </tr> <tr> <td>D)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>y</mi></mrow></mfrac><mo>=</mo><mi>y</mi></math></td> <td>s)</td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>c</mi></math></td> </tr> </tbody> </table> <p> </p>

In column I differential equations are given in column II their solutions are given then match them

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Solution

Q.
In column I differential equations are given in column II their solutions are given then match them

Column I Column II

A) $y \frac{d y}{d x} + x = 0$ p) $2 y = x^{2} + c$

B) $x \frac{d y}{d x} + y = 0$ q) $x^{2} + y^{2} = c$

C) $\frac{d y}{d x} = x$ r) $x y = c$

D) $\frac{d x}{d y} = y$ s) $y^{2} = 2 x + c$

Solution

1 A – r, B – q, C – p, D – s

2 A – q, B – r, C – p, D – s

3 A – s, B – q, C – p, D – r

4 A – p, B – q, C – r, D – s

Ans.
(2)

Use variable seperable

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	Column I		Column II
A)	$y \frac{d y}{d x} + x = 0$	p)	$2 y = x^{2} + c$
B)	$x \frac{d y}{d x} + y = 0$	q)	$x^{2} + y^{2} = c$
C)	$\frac{d y}{d x} = x$	r)	$x y = c$
D)	$\frac{d x}{d y} = y$	s)	$y^{2} = 2 x + c$

Solution

Q. In column I differential equations are given in column II their solutions are given then match them Column I Column II A) ydydx+x=0 p) 2y=x2+c B) xdydx+y=0 q) x2+y2=c C) dydx=x r) xy=c D) dxdy=y s) y2=2x+c

1 A – r, B – q, C – p, D – s

2 A – q, B – r, C – p, D – s

3 A – s, B – q, C – p, D – r

4 A – p, B – q, C – r, D – s

Ans. (2) Use variable seperable

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Ans.
(2)

Use variable seperable