Math Problem Statement
Solving Homogeneous Equations For equations of the form: a (d^2 y)/(dt^2 ) +dy/dt+cy=0 the characteristic equation is ar^2+br+c=0. Solutions depend on the nature of the roots:
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Differential Equations
Homogeneous Equations
Characteristic Equation
Quadratic Equations
Formulas
a \frac{d^2 y}{dt^2} + b \frac{dy}{dt} + c y = 0
a r^2 + b r + c = 0
\Delta = b^2 - 4ac
Theorems
Quadratic Roots Theorem
Discriminant of a Quadratic Equation
Suitable Grade Level
Undergraduate Mathematics or Advanced High School
Related Recommendation
Solving Systems of Differential Equations: Linear and Second-Order Equations
General Solutions to Second-Order Linear Homogeneous Differential Equations
Solving System of Second-Order Differential Equations
Solving Second-Order Linear Homogeneous Differential Equations
Solve 9y'' - 12y' + 4y = 0: Characteristic Equation and General Solution