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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The general solution of the differential equation $x d y-\left(1+x^2\right) d x=d x$ is :
  • A
    $y=2 x+\frac{x^3}{3}+C$
  • B
    $y=2 \log x+\frac{x^3}{3}+C$
  • C
    $y=\frac{x^2}{2}+C$
  • D
    $y=2 \log x+\frac{x^2}{2}+C$
✓

Answer

Given differential equation is
$
\begin{aligned}
x d y-\left(1+x^2\right) d x & =d x \\
\Rightarrow \quad x d y & =d x+\left(1+x^2\right) d x \\
& =\left(2+x^2\right) d x \\
\Rightarrow \quad d y & =\left(\frac{2}{x}+x\right) d x
\end{aligned}
$
Integrating both sides, we get
$
\begin{array}{l}
\int d y=\int\left(\frac{2}{x}+x\right) d x \\
\Rightarrow \quad y=2 \log x+\frac{x^2}{2}+C
\end{array}$

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