Differential Equations: One-Page Formula Sheet

Differential Equations — formula sheet

Formulas

• IF = e^(∫P dx)
• Solution: y·IF = ∫Q·IF dx + C
• Number of arbitrary constants = order
• Exact form: d(xy) = x dy + y dx

Key ideas

• Order = highest derivative; degree = its power after removing radicals
• Separate variables when possible
• Homogeneous: substitute y = vx
• Linear: dy/dx + Py = Q uses an integrating factor

Traps to avoid

• Degree undefined when derivatives sit inside sin or log
• Forgetting the constant before applying initial conditions
• Wrong integrating factor sign

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