.: We have, y = Ax …(1) Differentiating (1) w.r.t. x , we get y' = A …(2) Dividing (2) by (1), we get y = x xy' = y Hence, y = Ax is a solution of the given differential equation.

Differential Equations — Class 12 Maths Solution

ncert exercise SA NCERT Ex.9.2,Q.5,Page 385

Question

$y = Ax:xy' = y(x \ne 0)$

Step-by-step Solution

.: We have, $y = Ax$

…(1)
Differentiating (1) w.r.t. $x$,

we get $y' = A$

…(2)
Dividing (2) by (1),

we get $\cfrac{{y'}}{y} = \cfrac{1}{x} \Rightarrow xy' = y$

Hence, $y = Ax$ is a solution of the given differential equation.

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.