Write each of the following higher order equations as an equivalent first-order system of ODEs. Transform the system into vector form x′ = F(t, x). (a) Van der Pol equation: y′′ = y′(1 − y2) − y (b) Blasius equation: y′′′ = −yy′′ (c) Equation y′′′′ + (1 + t)y′′ − cos(y′)y = 2t^2
Write each of the following higher order equations as an equivalent first-order system of ODEs. Transform the system into vector form x′ = F(t, x). (a) Van der Pol equation: y′′ = y′(1 − y2) − y (b) Blasius equation: y′′′ = −yy′′ (c) Equation y′′′′ + (1 + t)y′′ − cos(y′)y = 2t^2
Write each of the following higher order equations as an equivalent first-order system of ODEs. Transform the system into vector form x′ = F(t, x). (a) Van der Pol equation: y′′ = y′(1 − y2) − y (b) Blasius equation: y′′′ = −yy′′ (c) Equation y′′′′ + (1 + t)y′′ − cos(y′)y = 2t^2
Write each of the following higher order equations as an equivalent first-order system of ODEs. Transform the system into vector form x′ = F(t, x). (a) Van der Pol equation: y′′ = y′(1 − y2) − y (b) Blasius equation: y′′′ = −yy′′ (c) Equation y′′′′ + (1 + t)y′′ − cos(y′)y = 2t^2
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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