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Exercise 101

Avg difficulty 2.5

Solve the following exact equations, implicit general solutions will suffice:

$\cos(x)+ye^{xy} + xe^{xy} y' = 0$
$(2x+y)\, dx + (x-4y) \, dy = 0$
$e^x + e^y \frac{dy}{dx} = 0$
$(3x^2+3y)\,dx + (3y^2+3x)\, dy = 0$

Lebl, Notes on Diffy Qs, §1.8 Exact equations, exercise 101

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Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.