Question
The family $Y = Ax + {A^3}$ of curves will correspond to a differential equation of order
- (a) 3
- (b) 2
- (c) 1 ✓ Correct
- (d) not defined
Differential Equations — Class 12 Maths Solution
Step-by-step Solution
Given family of curves is $y = Ax + {A^3}$
….(i)
$\Rightarrow$ $\frac{{dy}}{{dx}} = A$
Replacing $A$ by $\frac{{dy}}{{dx}}$ in Eq. (i),
we get
$y = x\frac{{dy}}{{dx}} + {\left( {\frac{{dy}}{{dx}}} \right)^3}$
$\therefore$ Order $= 1$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Differential Equations. Curated by Sachin Sharma. Free for all students.