For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1,...

For the diﬀerential equation x′′ + (o.1)(1 − x2)x′ + x = 0; x(0) = 1, x′(0) = 0. (a) Rewrite it as a system of ﬁrst order diﬀerential equations in preparation to solve with the vectorized version of a numerical approximation technique. (b) Use the vectorized Euler method with h = 0.2 to plot out an approximate solution for t = 0 to t = 10. (c) Plot the points to the approximated solution (make a scatter plot), make a prediction of what type of function the solution might be.

Expert Solution

samet mamat answered 2 years ago

Solve the wave equation, a2 ∂2u ∂x2 = ∂2u ∂t2 0 < x < L, t...

Solve the wave equation, a2 ∂2u ∂x2 = ∂2u ∂t2 0 < x < L, t > 0 (see (1) in Section 12.4) subject to the given conditions. u(0, t) = 0, u(π, t) = 0, t > 0 u(x, 0) = 0.01 sin(9πx), ∂u ∂t t = 0 = 0, 0 < x < π u(x, t) = + ∞ n = 1

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sin(tan-1 x), where |x| < 1, is equal to: (a) x/√(1 – x2) (b) 1/√(1 – x2) (c) 1/√(1 + x2) (d) x/√(1 + x2)

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1. Let X1, X2 be i.i.d with this distribution: f(x) = 3e cx, x ≥ 0...

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Consider the following differential equation: x2y"-2xy'+(x2+2)y=0 Given that y1=x cos x is a solution, find a...

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