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Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations2 Marks
Question
Form the differential equation from the following primitives where constants are arbitrart:$\text{y}^2=4\text{ax}$
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Answer

The equation of family of curves is
$\text{y}^2=4\text{ax}$
where a is an arbitrary constant. This equation contains only one arbitrary constant, so we shall get a differential equation of first order.
Differentiating equation (1) with respect to x, we get
$2\text{y}\frac{\text{dy}}{\text{dx}}=4\text{a}$
$\Rightarrow\frac{\text{y}}{2}\frac{\text{dy}}{\text{dx}}=\text{a}\ ...(2)$
Putting the value of a in equation (1), we get
$\text{y}^2=4\frac{\text{y}}{2}\frac{\text{dy}}{\text{dx}}\text{x}$
$\Rightarrow\text{y}=2\text{x}\frac{\text{dy}}{\text{dx}}$
It is the required differential equation.

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