Homogeneous First-Order Linear Differential Equation

A Homogenous First-order Linear Differential Equation is a First-Order Linear Differential Equation which equals to zero.

• Context:
  • It can be expressed as

[math]\displaystyle{ a_1(t)\frac{dy}{dt}+a_0(t)y=0\qquad\iff \qquad p(t)\frac{dy}{dt}+q(t)y=0 }[/math]

Alternatively, these expressions can be written as

[math]\displaystyle{ a_1(t)y'+a_0(t)y=0\quad\iff \quad y'+q(t)y=0\quad\textrm{with}\quad y''=\frac{d^2y}{dt^2},\;y'=\frac{dy}{dt} }[/math]

• Example(s):
  • Exponential Decay.
  • Exponential Growth.
• Counter-Example(s):
  • Inhomogenous Second-Order Linear Differential Equation.
  • Homogeneous Second-Order Linear Differential Equation.
  • Inhomogeneous First-Order Linear Differential Equation.
  • Polynomial Equation.
• See: Second-order Linear Differential Equation, First-Order Linear Differential Equation, Differential Equation, Linear Function.

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