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DiffEqs

# DiffEqs - Math 54 ODE review1 1 Separable Equations When to...

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Math 54 ODE review 1 1. Separable Equations When to use: When you can write it as y 0 = 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, it’s a pretty good hint its probably separable (since it’s not linear). Don’t forget about the constant solutions you get from solving f ( y ) = 0 Remember your +C’s! 2. Linear (First-Order) DiffEqs When to use: When it’s not separable and y 00 doesn’t appear anywhere. How to solve: Rewrite equation in the form y 0 + 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 0 are never squared, cubed, square-rooted, etc. Remember your +C’s! 3. Linear Second-Order Homogeneous DiffEqs When to use: Whenever y 00 shows up. How to solve: Write as ay 00 + by 0 + cy = 0 ( a, b, c must be constants) and solve the equation ar 2 + br + c = 0.

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DiffEqs - Math 54 ODE review1 1 Separable Equations When to...

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