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Other Math Archive: Questions from May 11, 2022

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  Find the gradient vector field of f. f(x, y, z) = 8√² + x² + y² + 2² 2 2 z Vf(x, y, z) =
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  Exercise 3 Solve the following separable variable differential equations: y.cos” < • ctg y + tgx siny = 0, y =y (2); ry' = y +ya, y=y (2); myy' = 1-22, y = y(); y' = (y + x)?, y=y(); y V = (8.x +
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  Exercise 4 Solve the following homogenuous differential equations: ry' = y - x, y = y(x); y = -(y + ), y=y (2); 22. y' = y2-y), y = y(); 2.ry. y' = ya +2+, y = y(x); (2xy - 2 y = -4, y = y(); Iy= y +
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  Exercise 6 Solve the following linear differential equations: 1-2.0 y' = y = 1, y=y (2); .2 3 e2-1 23 y' + 2xy = 2xe-r?, y=y(2); V + -y= y = y(x); y' + 2xy + x - e-r? = 0, y = y(x); ry' - ny=.”+1 In
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• PLEASE EXPLAIN EACH EXERCISE. Thanks!
  True or false. Determine if the following statements are true or false 1. El radio de convergencia de la serire immes R = 100 . 2. La función f(t) = 2t - e? es de orden exponencial y por lo tanto se
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  2. [6 pts.] Halla la solución de la ecuación diferencial y" + 2x(y')2 = 0.
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  3. [8 pts.] Halla una solución en series de potencias para la ecuación diferencial (x - 2)y" - y = 0, alrededor de x = 0.
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• Use la transformada de Laplace para resolver la ecuación diferencial. y'-2y=te4t y(0)=3
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  (2) Solve the D.E (i) 4y"+y=0 (ii) y" + y' - 2y = 0 y(0) = 4 y'(0) = 1 (iii) 4y" + 4y' - 7y = 0 (iv) y" – 4y' + 4y = 0 - y(0) = 3, = y'(0) = 1 = (3) Solve The D.E (i) y" + 4y = 8x2 (ii) y" – 4y' +
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  (3) Solve The D.E (i) y' + 4y = 8x2 = (ii) y" – 4y' + 3y = 10 e -2x (iii) y" – y' – 2y = 10 cos (x) (iv) y" – 3y' +2y=4x + 3x (v) y" – 4y = x sin(2x)
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• Solve the system: dx/dt = x' = 9x + 4y dy/dt = y' = -6x - y dz/dt = z' = 6x + 4y + 3
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