State the order of the given ordinary differential equation. d^2u/dr^2 + du/dr + u = cos(r + u) Determine whether the equation is linear or nonlinear by matching it with (6) in Section 1.1. an(x) d^ny/dx^n + an-1(x) d^n-1y/dx^n-1 + ... + a1(x) dy/dx + a0(x)y = g(x) (6) linear nonlinear
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The order of an ordinary differential equation is determined by the highest derivative present in the equation. In this case, the highest derivative is the second derivative, d^2u/dr^2. Therefore, the order of the given ordinary differential equation is 2. Show more…
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