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Differential Equation and Applications (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Differential Equation and Applications (p-1)2 Marks
Question
Form the differential equation by eliminating arbitrary constants from the relation $b x+a y=a b$.
✓

Answer

$
\begin{aligned}
& b x+a y=a b \\
& \therefore a y=-b x+a b \\
& \therefore y=-\frac{b}{a} x+b
\end{aligned}
$
Differentiating w.r.t. $x$, we get
$
\frac{d y}{d x}=-\frac{b}{a} \times 1+0=-\frac{b}{a}
$
Differentiating again w.r.t. $x$, we get $\frac{d^2 y}{d x^2}=0$ is the required D.E.

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