Introduction to Differential Equations Math Example 4

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Example 4

medium
Find the particular solution to y′=−2yy' = -2y with y(0)=3y(0)=3.

Solution

  1. 1
    General: y=Ce−2xy = Ce^{-2x}. y(0)=3⇒C=3y(0)=3 \Rightarrow C=3.
  2. 2
    Particular: y=3e−2xy = 3e^{-2x}.

Answer

y=3e−2xy = 3e^{-2x}
Exponential decay: y′=−2yy' = -2y has solution Ce−2xCe^{-2x}. IC sets C=3C=3.

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 1 easy

Verify [formula] solves [formula], and find the particular solution with [formula].

Example 2 medium

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

Example 3 easy

Verify that [formula] satisfies [formula].

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