Which of the following equation is linear - Vidyadip

MCQ

Which of the following equation is linear

A
$\frac{{dy}}{{dx}} + x{y^2} = 1$
✓
${x^2}\frac{{dy}}{{dx}} + y = {e^x}$
C
$\frac{{dy}}{{dx}} + 3y = x{y^2}$
D
$x\frac{{dy}}{{dx}} + {y^2} = \sin x$

✓

Answer

Correct option: B.

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

b
(b) ${x^2}\frac{{dy}}{{dx}} + y = {e^x}$ can be written as

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

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