The solution of the differential equation 2 x d y d x - y =3 repr… - Vidyadip

MCQ

The solution of the differential equation $2 x \frac{d y}{d x}- y =3$ represents:

✓
parabolas
B
straight lines
C
ellipses
D
circles

✓

Answer

Correct option: A.

parabolas

(a) parabolas
Explanation: $2 x \frac{d y}{d x}= y +3 \Rightarrow \frac{d y}{d x}=\frac{y+3}{2 x} \Rightarrow \frac{2 \frac{d y}{d x}}{y+3}=\frac{1}{x}$
Integration both sides
$
\begin{array}{l}
\int \frac{2 \frac{d y}{d x}}{y+3}=\int \frac{1}{x} \\
\Rightarrow 2 \log (y+3)=\log x+c \\
\Rightarrow(y+3)^2=x+c
\end{array}
$

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