In Exercises 53-60. find the particular solution of each system of differemial equations thlll satisfies the given initial conditions. 60 )'; = 5)'t - 2)'2 - 2y; y; = 18yt - 7yz - 6y3 y~ = -6yt + 2yz + '3with Yt(O) = 4, yz(O) = 5. )'3(0) = 8
1.3 Solving Equations Definition: two equations are equivalent if they share the same solutions. Definition: a, b, c ∈ R 1. a = b i s Equivalent to a + c = b + c 2. a = b quivalent t o ac = b c≠0) Example: y + 4.3 = 11.2→ y = 11.2 - 4.3 → y = 6.9 Definition: Linear Equation: T ypes o f Solutions: 1. Solution set i s R, identity Example: 2x + 2 → 0 = 0 2. olution s et is , contradiction Example: x + = 3 x = → 0 = 1 3. nique solution, c
