Cheatography

# Differential Equations Cheat Sheet by stoneoxmike

Differential Equations Exam 1

### Recognize the Type

 1. First check to see if it is separable. 2. Next check to see if it is linear by looking at what is being done to the dependent variable and its deriva­tives. 3. If it is not linear, but looks close, try Bernoulli form. 4. Next, try checking for exactness. 5. If x and y are only to the first power with the same coeffi­cients, try substi­tution. 6. If none of these work, try checking if it is separable again.

### Separable Linear Equations

 1. Check that the dependent variable (the one having its derivative taken) is only to the first power. 2. Check that the dependent variable is not in a function (trig, expone­ntial, log). 3. Check that equation can be reorga­nized so that each variable is on opposite sides by itself. 4. Integrate both sides and solve for dependent variable (don't forget C).

### Non-se­parable Linear Equations

 1. Reorganize into general form: . . . 2. Find the integr­ating factor: . . . 3. Use integr­ating factor in solved formula: . . .

### Bernoulli Equations

 1. Reorganize equation into general form: . . . 2. Substitute v: . . . 3. Solve resulting linear equation: . . . 4. Solve for v and resubs­titute.

### Exact Equations

 1. Reorganize into general form: . . . 2. Test for exactness with partial deriva­tives: . . . 3. Find f(x,y) for both M and N with partial integr­ation: . . . 4. Find the general solution, including any terms that are missing from either integr­ation: . . .

### Substi­tution Equations

 1. Reorganize into general form: . . . 2. Let z equal: . . . 3. Find dz/dx: . . . 4. Substitute and solve resulting separable equation for dy/dx.