Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. (i) f(x) = 1 (ii) f(x) = e¬X (ii) f(x) = eX (iv) f(x) = sin 2x (v) f(x) = ex sin x...

Extracted text: Without solving, match a solution curve of y" + y = f(x) shown in the figure with one of the following functions. (i) f(x) = 1 (ii) f(x) = e¬X (ii) f(x) = eX (iv) f(x) = sin 2x (v) f(x) = ex sin x (vi) f(x) = sin x Briefly discuss your reasoning. (a) We see that the solution is the sum of a sinusoidal term and a term that o is sinusoidal with a different period. is constant and simply translates the sinusoidal part vertically. goes to o as x → ∞ and 0 as x → -∞. o goes to 0 as x → o and o as x → -o. o oscillates with an amplitude that goes to o as x → and 0 as x → -0. (b) We see that the solution is the sum of a sinusoidal term and a term that o is sinusoidal with a different period. is constant and simply translates the sinusoidal part vertically. goes to o as x → o and 0 as x → -o. goes to 0 as x → ∞ and ∞ as x → -o. oscillates with an amplitude that goes to ∞ as x → o and 0 as x → -o. (c) ?


Extracted text: We see that the solution is the sum of a sinusoidal term and a term that o is sinusoidal with a different period. o is constant and simply translates the sinusoidal part vertically. o goes to o as x → ∞ and 0 as x → -. o goes to 0 as x → o and o as x → -o. o oscillates with an amplitude that goes to o as x → ∞ and 0 as x → -o. (d) ? We see that the solution is the sum of a sinusoidal term and a term that o is sinusoidal with a different period. o is constant and simply translates the sinusoidal part vertically. o goes to o as x → ∞ and 0 as x → -o. o goes to 0 as x → ∞ and ∞ as x → -∞. oscillates with an amplitude that goes to o as x → ∞ and 0 as x → -∞.