Consider the equation (y² + xy³) dx + (5y² – xy + y³ sin y) dy = 0 • Show that the original DE is not exact.(That is, use test for exactness) • Determine an integrating factor that will make the new differential equation, exact. • Show that the resulting equation is now exact and then determine the one-parameter family of solution for the given differential equation.

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Chapter1: Functions And Models
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Consider the equation (y² + xy³)dx + (5y² – xy + y³ sin y) dy = 0
• Show that the original DE is not exact. (That is, use test for exactness)
• Determine an integrating factor that will make the new differential equation, exact.
• Show that the resulting equation is now exact and then determine the one-parameter family
of solution for the given differential equation.
Transcribed Image Text:Consider the equation (y² + xy³)dx + (5y² – xy + y³ sin y) dy = 0 • Show that the original DE is not exact. (That is, use test for exactness) • Determine an integrating factor that will make the new differential equation, exact. • Show that the resulting equation is now exact and then determine the one-parameter family of solution for the given differential equation.
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