Introduction to Differential Equations Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Verify y=3e2xy = 3e^{2x} solves y′=2yy' = 2y, and find the particular solution with y(0)=5y(0) = 5.

Solution

  1. 1
    y′=6e2x=2(3e2x)=2yy' = 6e^{2x} = 2(3e^{2x}) = 2y. ✓
  2. 2
    General: y=Ce2xy = Ce^{2x}. Apply y(0)=5y(0)=5: C=5C=5.
  3. 3
    Particular: y=5e2xy = 5e^{2x}.

Answer

Verified; particular solution y=5e2xy = 5e^{2x}
Verify by substitution; the initial condition pins down CC.

About Introduction to Differential Equations

An equation that contains an unknown function and one or more of its derivatives. Solving a DE means finding the function(s) that satisfy the equation.

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More Introduction to Differential Equations Examples

Example 2 medium

Find the general and particular ([formula]) solution to [formula].

Example 3 easy

Verify that [formula] satisfies [formula].

Example 4 medium

Find the particular solution to [formula] with [formula].

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