## Problem 05 | Substitution Suggested by the Equation

**Problem 05**

$dy/dx = \sin (x + y)$

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**Problem 05**

$dy/dx = \sin (x + y)$

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**Problem 03**

$dy/dx = (9x + 4y + 1)^2$

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**Problem 02**

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

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**Problem 01**

$(3x - 2y + 1)~dx + (3x - 2y + 3)~dy = 0$

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Problem 06 - 07 | Integrating Factors Found by Inspection

**Problem 06**

$y(y^2 + 1) \, dx + x(y^2 - 1) \, dy = 0$

**Problem 07**

$y(y^2 + 1) \, dx + x(y^2 - 1) \, dy = 0$

**Problem 22**

$(xy + x) \, dx = (x^2y^2 + x^2 + y^2 + 1) \, dy = 0$

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**Problem 21**

$x^2 \, dx + y(x - 1) \, dy = 0$

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**Problem 20**

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

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**Problem 19**

$dr = b(\cos \theta \, dr + r \sin \theta \, d\theta)$

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**Problem 18**

$ye^{2x} \, dx = (4 + e^{2x}) \, dy$

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