QUESTION 1 dy = 8e - x - is a first order differential equation. dx O True O FalseQUESTION 2 dy Find the particular solution of the initial value problem 2- = Axe *; y (0) =5 dx O y=7+ 2xe * - 20 * O v=7-2xe * - 2e O y=5+ 2xe -* - 2e O y=5- 2xe - 2eQUESTION 3 dy Find the particular solution of the initial value problem - + 3x2= 2x; y (0) =5 dx Oy=5-x3+x2 Oy=5+x3-x2 Oy=C+x3-x2 Ov=5+x3+x2 QUESTION 4 The above is an "explicit solution", i.e., it gives y directly as a function of x. O True FalseQUESTION 5 The above is an "implicit solution", i.e., it gives y as an implicit function of x. O True False QUESTION 6 The differential equation dy = Be - x2 adx is a separable since it can be converted into the following integral equation O True O FalseQUESTION 7 The differential equation dy dx is separable because it can be written as: O ey dy = e dx fed = le -5x dx O O e Sy dy = e -x dxQUESTION 8 The differential equation dy =e dx is separable. O True O FalseQUESTION 9 Using the results above, find the solution to the following initial value problem dy =e - 3+Y Y(0) =0 ax O + O - Y - e UI O -Y - -e O -eQUESTION 10 Find the general solution of the differential equation dy adx O -5x + C 5x -e + C O e'=5e" + C O - 5x e eQUESTION 11 The general solution of the differential equation dy = Be dx is: O -e -X O V= e + - +C 3 O 4 -x 3 e + + 2 O 4 V= + -X 3- 2