For which of the cases below is the given two-parameter family of functions the general solution of the corresponding nonhomogeneous differential equation on the indicated interval? (i) y" – 7y' + 10y = 50x2 – 70x + 10; e2x + 5x², y = c1 ex + c2 (-00, 00) (il) у" — бу' + 9у —D 64 sin x - 8 cos x; y = cj e3x + c2 xe3x + 8sin x, (-∞, 0) (iii) x*y" – 20xy' + 110y 264; y = c1x10 + c2 x1 + 2, C1 X

To find the differential equation of y = c,e" cos 3x + c. -2x first derivative, we arrive at y'e-2x - 2 y e- ze sin 3x, we use elimination of constants. If by getting the — 3с, sin 3x + Зс, сos 3х, which of the differential equations is correct? A y" + 13 y - 4 y = 0 B y" - 4 y' + 13 y = 0 y" - 13 y' + 4y 0 у" + 4у' — 13 у%3D0

Consider the function of two variables  u (x,t) = 2e-t sin (2x)  Select the option that gives a partial differential equation for which this function of two variables is a solution.  A. (∂2u/∂x2) = 4(∂2u/∂t2)  B. (∂2u/∂x2) = (1/4)(∂2u/∂t2)  C. (∂2u/∂x2) = - (1/4)(∂2u/∂t2)  D. (∂2u/∂x2) = -4 (∂u/∂t)  E. (∂2u/∂x2) = 4 (∂u/∂t)

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