The solution of the equation d y d x +2 x=e^ 3 x is : - Vidyadip

MCQ

The solution of the equation $\frac{d y}{d x}+2 x=e^{3 x}$ is :

✓
$y+x^2=\frac{1}{3} e^{3 x}+c$
B
$y-x^2=\frac{1}{3} e^{3 x}+c$
C
$y+x^2=e^{3 x}+c$
D
$y-x^2=e^{3 x}+c$

✓

Answer

Correct option: A.

$y+x^2=\frac{1}{3} e^{3 x}+c$

(A)
$
\begin{aligned}
& \\
\Rightarrow \quad \frac{d y}{d x}+2 x & =e^{3 x} \\
\frac{d y}{d x} & =e^{3 x}-2 x \\
d y & =\left(e^{3 x}-2 x\right) d x \\
\therefore \quad \int d y & =\int\left(e^{3 x}-2 x\right) d x \\
y & =\frac{1}{3} e^{3 x}-\frac{2 x^2}{2}+C \\
y & =\frac{1}{3} e^{3 x}-x^2+C \\
\Rightarrow \quad y+x^2 & =\frac{1}{3} e^{3 x}+C
\end{aligned}
$
Hence the correct choice is (A).

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