7. y = Cex - 5; DE: " = y +5 For each differential equation, find the particular solution that passes through the given point or meets the initial value conditions. 3 + 6x2; (1,1) 8. - = 2-x 9 ax = =e2x - 3x2 + 1; y(0) => 10. dy = 12 cos(4x) - ex; y(0) = 17.1 Practice: Intro to Differential Equations Write a differential equation that describes each relationship. 1. The rate of growth of a certain bacteria B, in a petri dish is proportional to the numb of bacteria in the dish. dB . = KB 2. An object moves along a straight line. Its speed S, is inversely proportional to the square of the distance D, the object traveled. 3. The rate of growth of a population of grasshopper, P, is inversely proportional to the square root of the population. Verify the solution of the differential equation. 4. y = e-4x; DE: y" + 3y' = 4y y = - geg x 16 2 9x + 3 ( - he (* ) = 4 ( 2 9 * ) y = 16 e- 4 x 16 84x - 12 89x = 4 e-9x "* = Genx V 5. y = esin (x); DE: y' = ycos(x) 6. 3x2 + 2y2 = C; DE: 3x + 2yy' = 0