Question

Homework 01: Differential Equation Review Due 2020-01-15 Solve for yio the following equations 1 = -2 2. - 700)=2 3. = [0) = 3 (1) = 2 4 -3 710) - (1) - 1 5.33 - 5y = 0 (0-0; y(1) - 1 6. #+y=0 [+1) = 2 7. * +22- 0 0 ) - 1: () = 0 Hints . If in E = constant then T) I r - 2 We can defne w constant that . The solution - de' + eye H etimien lewds to a clear is equivalent to the solution tior. - Char c oal, which . Note that Problem # 7 L na closed for solution, but instead should be lett andet nite integral. It can be list transformed into a Ist order differential equation through the substitution / solved lor / and then substituted before solving for

solve for y

Answer 1

0 Given that -dy=4_-1___ 4.00u = 2 talking integration on both sides we get dx Y(2) = 40 + 6 y (0) = 4(0) + 6 2 =c - ( 4 103=2 si ey becomes (n) = 4x + 2 This is required soll of eq? - Jy dey y 102=2 we can write it as is its Quxiliary: ey M-1 0 ma! . Its . son is 40.2 = cenu. yo) = ci e ac . 2:6, soln is yu) = 2 e

Given that 0 .4409-3-4113 = 2 Jorking integration y = 61 tl y'CM)=(: Terking integredios dil Y()'. Ci 4+ (2 : y 10:01 3 C) ¢ y(i)= (1+(? 2 3 +62 > 622-1 - 1. Y(u) = 3x -/ . - ola2 L z dy : 3 y,0) = 4 yout os integration => - 32 +6; 3+447 00_jötegration yu) = 3x² +62 +6 2

4 = ر ( ر) حمله نيواو ) که في من ا ) از ب) - (ا - - ي) = ر- فيك+ 3 = (1)