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Unformatted text preview: Math 54 ODE review 1 1. Separable Equations When to use: When you can write it as y = f ( y ) g ( x ). How to solve: Rewrite as dy f ( y ) = g ( x )dx and integrate both sides. Reminders, Tips, and Tricks: Separable things are good, so always check this first. If there are things like y 2 floating around, its a pretty good hint its probably separable (since its not linear). Dont forget about the constant solutions you get from solving f ( y ) = 0 Remember your +Cs! 2. Linear (First-Order) DiffEqs When to use: When its not separable and y 00 doesnt appear anywhere. How to solve: Rewrite equation in the form y + P ( x ) y = Q ( x ) and compute I = e R P ( x ) dx . Then y = R IQdx I Reminders, Tips, and Tricks: Linear means that y and y are never squared, cubed, square-rooted, etc. Remember your +Cs! 3. Linear Second-Order Homogeneous DiffEqs When to use: Whenever y 00 shows up....
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