Chapter Contents

• Differential Equations
• Predicting AIDS - a DEs example
• 1. Solving Differential Equations
• 2. Separation of Variables
• 3. Integrable Combinations
• 4. Linear DEs of Order 1
• 5. Application: RL Circuits
• 6. Application: RC Circuits
• 7. Second Order DEs - Homogeneous
• 8. Second Order DEs - Damping - RLC
• 9. Second Order DEs - Forced Response
• 10. Second Order DEs - Solve Using SNB
• Differential Equations Problem Solver

• Comments, Questions?

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4. Linear DEs of Order 1

If P = P(x) and Q = Q(x) are functions of x only, then

is called a linear differential equation order 1.

We can solve these linear DEs using an integrating factor.

For linear DEs of order 1, the integrating factor is: e^∫Pdx

The solution for the DE is given by multiplying y by the integrating factor (on the left) and multiplying Q by the integrating factor (on the right) and integrating the right side with respect to x, as follows:

Example 1

Solve

Answer

Example 2

Solve

Answer

Example 3

Solve dy + 3ydx = e^−3xdx

Answer

Example 4

Solve 2(y - 4x²)dx + x dy = 0

Answer

Example 5

Solve

Answer