By Valentina Giambanco

Un cielo tan azul que duele mirarlo. Árboles centenarios de más de treinta metros de altura. El niño corre descalzo. Se detiene en un pequeño claro, jadeando, y escucha. Tiene as soon as, puede que doce años, y los ojos desorbitados. Sus vaqueros muestran desgarros, l. a. camiseta gris está empapada en sudor y las mangas se pegan a sus escuálidos brazos. Los cortes en los angeles tela dejan ver su piel, y l. a. sangre le cubre los brazos. Se aparta un mechón de pelo de los ojos y vomita lo poco que le queda en el estómago. Se apoya en un árbol y luego cae. Arrastrado por los angeles gravedad, su cuerpo pierde el equilibrio y se abre paso entre las hojas caídas. l. a. tierra cruje y se mueve bajo sus pies. Seattle. Han pasado veinticinco años desde que tres niños fueron raptados en el bosque; sólo dos volvieron con vida, el cuerpo del tercero nunca se recuperó y su muerte y el misterio de lo que ocurrió aquel día han marcado las vidas de todos los implicados. Dos semanas antes de Navidad una familia aparece asesinada en su casa. Todas las pruebas apuntan a un hombre temido a ambos lados de l. a. ley: John Cameron. Él fue uno de los niños que sobrevivió al secuestro; el otro period el padre de l. a. familia muerta. El asesino ha dejado un mensaje grabado en el marco de una puerta: TRECE DÍAS. Es el tiempo que concede a los angeles detective de homicidios Alice Madison para que comprenda su propósito y cumpla el papel que le tiene destinado. Ahora ella, para atrapar al psicópata que está detrás de estas muertes, debe traicionar a sus compañeros y hacer un pacto con el diablo. A los trece días, l. a. línea entre el bien y el mal se desdibuja en los angeles lucha por alcanzar los angeles justicia.

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M P /j D rt C k; where k is the constant of integration. Using the same algebraic techniques employed in Example 4 and the earlier examples on radioactive decay and Newton’s law of cooling, we get P m P D cert ; for some real constant c. 3 Separable Differential Equations 39 where the second equation is obtained from the first by multiplying the numerator and denominator by e rt . t/ D 0 is obtained by setting c D 0. t/ D m does not occur for any choice of c, so this solution is an extra one. 1 e cm cm D D m; Cc c rt independent of c ¤ 0.

Example 2. Draw the direction field for the differential equation yy 0 D t. Draw several solution curves on the direction field and deduce the family of solutions. I Solution. Before we can draw the direction field, it is necessary to first put the differential equation yy 0 D t into standard form by solving for y 0 . Solving for y 0 gives the equation y0 D t : y (2) Notice that this equation is not defined for y D 0, even though the original equation is. Thus, we should be alert to potential problems arising from this defect.

38. t; y/-plane. t0 // provides us with an elementary and often very effective method for the visualization of the solution curves (WD graphs of solutions) to (1). The visualization process involves the construction of what is known as a direction field or slope field for the differential equation. For this construction, we proceed as follows. Construction of Direction Fields 1. t; y/. 2. t; y/ is defined. This means imposing a graph-paperlike grid of vertical lines t D ti for a D t1 < t2 < < tN D b and horizontal lines y D yj for c D y1 < y1 < < yM D d .

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