Ch 11/Simultaneous Differential Equations/H.K. Dass 3.31

Simultaneous Differential Equations

When two dependent variables are functions of a single independent variable with linked derivatives, eliminate one variable to get a single ODE, solve, then back-substitute.

IWorking Rule

1. Write equations using .

2. Eliminate (or ) algebraically.

3. Solve the resulting single ODE.

4. Find the other variable by substituting back into an ORIGINAL equation.

Note

Always find the second variable by substituting back. Do not solve from scratch.

Example 1easy

Solve , .

Show step-by-step solution+

Eliminate y

. A.E.: .

x

y from equation (1)

Example 2medium

Solve , , with .

Show step-by-step solution+

Eliminate to get

Solve

Apply conditions

Answer

, .

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