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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 $\frac{\text{y}\ \text{dx}-\text{x}\ \text{dx}}{\text{y}}=0$ 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
$\frac{\text{y dx}-\text{x dy}}{\text{y}}=0$
or $\frac{\text{y dx}-\text{x dy}}{\text{x}^2}=0$ or $\text{d}\Big(\frac{​​​\text{x}}{​​​\text{y}}\Big)=0$
$\therefore\ \ \frac{​​​\text{x}}{​​​\text{y}}=​​​$constant.
$\therefore\ \ \frac{​​​\text{x}}{​​​\text{y}}=​​​\text{C}$ or ​​​$\text{y}=​​​\text{Cx}$
$\therefore\ \text{(C)}$ is correct answer.
The given differential equation is
$\frac{​​​\text{y dx}-​​​\text{x dy}}{​​​\text{y}}=0$
or $\frac{\text{y dx}-\text{x dy}}{\text{x}^2}=0$ or $\text{d}\Big(\frac{\text{x}}{\text{y}}\Big)=0$
$\therefore\ \ \frac{\text{x}}{\text{y}}=$constant.
$\therefore\ \ \frac{\text{y}}{\text{x}}=\text{C}$ or $\text{y}=\text{Cx}$

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