2. Verify that the functions y and y2 are solutions of each following differential equation. Then...

Transcribed Image Text:

2. Verify that the functions yı and y2 are solutions of each following differential equation. Then find a particular solution of the form y = c1yı + C2y2 that satisfies the given initial conditions. (Primes denote derivatives with respect to x.) (a) y" – y = 0; yı = e*, y2 = e*; y(0) = 0, y'(0) = 5 (b) у" — Зу' + 2y %3 0;B У1 %3D е*, Уз — е*; у(0) — 1, у'(0) — 0 (с) у" — 2у' + 2у 3 0;B У1 3 е\ сos x, У2 3D еX sin x; у(0) — 0, у'(0) — 5 (d) х*у" + ху+у 3D 0; У1 — сos(In x), У2 %3D %3D = e sin(In x); y(1) = 2, y'(1) = 3 2. Verify that the functions yı and y2 are solutions of each following differential equation. Then find a particular solution of the form y = c1yı + C2y2 that satisfies the given initial conditions. (Primes denote derivatives with respect to x.) (a) y" – y = 0; yı = e*, y2 = e*; y(0) = 0, y'(0) = 5 (b) у" — Зу' + 2y %3 0;B У1 %3D е*, Уз — е*; у(0) — 1, у'(0) — 0 (с) у" — 2у' + 2у 3 0;B У1 3 е\ сos x, У2 3D еX sin x; у(0) — 0, у'(0) — 5 (d) х*у" + ху+у 3D 0; У1 — сos(In x), У2 %3D %3D = e sin(In x); y(1) = 2, y'(1) = 3