Find the most general function M (x, y) so that the given differential equation is exact and...

Question:

Find the most general function {eq}M (x,\ y) {/eq} so that the given differential equation is exact and solve.

{eq}\displaystyle M (x,\ y)\ dx + (x^2 + 2 y)\ dy = 0 {/eq}.

Differential Equation:

Differential equation of form {eq}M(x,y) dx+N(x,y) dy=0 {/eq} is said to be exact when it satisfies the condition {eq}\displaystyle \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x} {/eq}.

And solution will be

{eq}\displaystyle \int _{y\:constant\:}M\:dx+\int _{No\:x\:term\:}N\:dy=C\:\: {/eq}

Answer and Explanation: 1

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Given exact differential equation is

{eq}\displaystyle M (x,\ y)\ dx + (x^2 + 2 y)\ dy = 0\\ {/eq}

It's satisfies the condition {eq}\displaystyle...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.


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