Homogeneous differential equation

kimkibun · May 2, 2012

how am i going to determine if a higher order differential equation is homogenous? example,

d⁴y/dx⁴+d²y/dx²=y

d³y/dx³-d²y/dx²=0

bigfooted · May 2, 2012

Homogeneous means all terms depend on y, no matter the order of the ODE. In your examples, both equations would be homogeneous. If you would add a term like 1 or f(x) it would become nonhomogeneous, i.e. y"=y is homogeneous, but y"=y+f(x) is nonhomogeneous.

Homogeneous differential equation

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

Undergrad Mixed approximation vs. full approximation for a power series expansion

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

High School Arc Length for Hyperbolic Sin

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Homogeneous differential equation

Similar threads