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DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS1 Mark
MCQ
The general solution of the differential equation $\frac{\text{y}\ \text{dx}-\text{x}\ \text{dx}}{\text{y}}=0\ \text{is}$
  • A
    $\text{xy}=\text{C}$
  • B
    $\text{x}=\text{Cy}^2$
  • ✓
    $\text{y}=\text{Cx}$
  • D
    $\text{y}=\text{Cx}^2$
✓

Answer

Correct option: C.
$\text{y}=\text{Cx}$
The given differential equation is

$\frac{\text{y dx}-\text{x dy}}{\text{y}}=0$

$​​​\text{or}\ \ ​\frac{\text{y dx}-\text{x dy}}{\text{x}^2}=0\ \ ​​​\text{or}\ \ ​​​\text{d}\Big(\frac{​​​\text{x}}{​​​\text{y}}\Big)=0$

$\therefore\ \ \frac{​​​\text{x}}{​​​\text{y}}=​​​\text{constant}.$

$\therefore\ \ \frac{​​​\text{x}}{​​​\text{y}}=​​​\text{C}\ ​​​\text{or}\ ​​​\text{y}=​​​\text{Cx}$

$\therefore\ \text{(C)}\ ​​​\text{is correct answer}.$

The given differential equation is

$\frac{​​​\text{y dx}-​​​\text{x dy}}{​​​\text{y}}=0$

$\text{or}\ \ \frac{\text{y dx}-\text{x dy}}{\text{x}^2}=0\ \ \text{or}\ \ \text{d}\Big(\frac{\text{x}}{\text{y}}\Big)=0$

$\therefore\ \ \frac{\text{x}}{\text{y}}=\text{constant}.$

$\therefore\ \ \frac{\text{y}}{\text{x}}=\text{C}\ \ \text{or}\ \ \text{y}=\text{Cx}$

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