## Problem 02 | Substitution Suggested by the Equation

**Problem 02**

$\sin y(x + \sin y)~dx + 2x^2 \cos y~dy = 0$

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**Problem 02**

$\sin y(x + \sin y)~dx + 2x^2 \cos y~dy = 0$

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**Problem 01**

$3(3x^2 + y^2) \, dx - 2xy \, dy = 0$

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**Problem 02**

$(x - 2y) \, dx + (2x + y) \, dy = 0$

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**Problem 03**

$2(2x^2 + y^2) \, dx - xy \, dy = 0$

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**Problem 04**

$xy \, dx - (x^2 + 3y^2) \, dy = 0$

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Given the differential equation

$M(x, y)\,dx + N(x, y)\,dy = 0$ ← Equation (1)

where *M* and *N* may be functions of both *x* and *y*. If the above equation can be transformed into the form

$f(x)\,dx + f(y)\,dy = 0$ ← Equation (2)

where *f*(*x*) is a function of *x* alone and *f*(*y*) is a function of *y* alone, equation (1) is called **variables separable**.

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