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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
Solve the following differential equations : $\frac{d y}{d x}+ y =3$
✓

Answer

$
\frac{d y}{d x}+ y =3
$
This is the linear differential equation of the form
$
\frac{d y}{d x}+P \cdot y=Q, \text { where } P=1, Q=3
$
$
\therefore \text { I.F. }=e^{\int P d x}=e^{\int 1 d x}=e^x
$
$\therefore$ the solution of (1) is given by
$
\begin{aligned}
& y \cdot\left(\text { I.F.) }=\int Q \text { (I.F.) } d x+c\right. \\
& \therefore y e^x=\int 3 e^x d x+c=3 e^x+c \\
& \therefore y e^x=3 e^x+c
\end{aligned}
$
This is the general solution.

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