The Euler Formula for Solving the System $y ^ { t } = u , u ^ { t } = f ( x , y , u ) , y \left( x _ { 0 } \right) = y _ { 0 } , u \left( x _ { 0 } \right) = u _ { 0 }$

question 2

Multiple Choice

The Euler formula for solving the system $y ^ { t } = u , u ^ { t } = f ( x , y , u ) , y \left( x _ { 0 } \right) = y _ { 0 } , u \left( x _ { 0 } \right) = u _ { 0 }$ is

• A) \(y _ { n + 1 } = y _ { n } + h u _ { n } , u _ { n + 1 } = u _ { n } + h f \left( x _ { n } , y _ { n } , u _ { n } \right)\)
• B) \(y _ { n + 1 } = y _ { n } - h u _ { n } , u _ { n + 1 } = u _ { n } + h f \left( x _ { n } , y _ { n } , u _ { n } \right)\)
• C) \(y _ { n + 1 } = y _ { n } + h u _ { n } , u _ { n + 1 } = u _ { n } - h f \left( x _ { n } , y _ { n } , u _ { n } \right)\)
• D) \(y _ { n + 1 } = y _ { n } + h f \left( x _ { n } , y _ { n } , u _ { n } \right) , u _ { n + 1 } = u _ { n } + h u _ { n }\)
• E) none of the above

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Definitions:

Pure Inductive

Refers to a circuit element or circuit that purely has inductance without any resistance, ideally opposing changes in current by generating a magnetic field.

Current

The rate of flow of electrons.

Coil

A component that produces a magnetic field when electric current flows through it.

Inductance

The property of an electrical conductor by which a change in current flowing through it induces an electromotive force in both that conductor and any nearby conductors.