Which of the following equation is linear?

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Solution

Q.
Which of the following equation is linear

1 $\frac{d y}{d x} + x y^{2} = 1$

2 $x^{2} \frac{d y}{d x} + y = e^{x}$

3 $\frac{d y}{d x} + 3 y = x y^{2}$

4 $x \frac{d y}{d x} + y^{2} = \sin x$

Ans.
(2)

Ans. $x^{2} \frac{d y}{d x} + y = e^{x}$

Explanation:

$x^{2} \frac{d y}{d x} + y = e^{x}$ can be written as

$\frac{d y}{d x} + \frac{y}{x^{2}} = \frac{e^{x}}{x^{2}},$ which is a linear equation.

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