Question

(3x+2y)dx+(2x+y)dy=0​

Answer 1

Answer:

It's a kind of Differential equation

Step-by-step explanation:

Check the attachment for your answer

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Answer 2

GIven: $\[\left( {3x + 2} \right)dx + \left( {2x + y} \right)dy = 0\]$.

To solve: the given expression.

Solution:

Simplify the given expression.

$\[\begin{array}{l}\left( {3x + 2} \right)dx + \left( {2x + y} \right)dy = 0\\ \Rightarrow \left( {3x + 2} \right)dx = - \left( {2x + y} \right)dy\end{array}\]$

Integrate both sides.

$\[\begin{array}{l} \Rightarrow \int {\left( {3x + 2} \right)dx} = - \int {\left( {2x + y} \right)dy} \\ \Rightarrow \frac{{3{x^2}}}{2} + 2x = - 2xy - \frac{{{y^2}}}{2}\\ \Rightarrow 3{x^2} + 4x = - 4xy - {y^2} + C\end{array}\]$