Esercizi di Analisi Mat. 2 - Esercizi e Dispense - Università degli ...

7. EQUAZIONI DIFFERENZIALI ORDINARIESol. es. 7.4 — y(x) = Ce x2 − 1Sol. es. 7.5 — y(x) = 1 cos (x) sin (x)−2x 2x 2 + C x 2Sol. es. 7.6 — y(x) = 1 2 + Ce−x2Sol. es. 7.7 — y(x) = 2 5 (x√ x + C x )Sol. es. 7.8 — y(x) = − 2 3 x cos2 (x) + 2 3 tan (x) − 2 9 tan (x) sin2 (x) + 1cos (x)Sol. es. 7.9 — y(x) = 1 8 (x5 − 1 x 3 )Sol. es. 7.10 — y(x) = e x3 x 4 + 2e x3− cos (x)Sol. es. 7.11 — y(x) = CeSol. es. 7.12 — y(x) = 1 3 ln ( 3 103x(sin (x) + 3 cos (x)) + C)1−Sol. es. 7.13 — y(x) = e Ce xSol. es. 7.14 — y(x) =tan (sin (x) + C)2Sol. es. 7.15 — y(x) = 1 + ( x24 + C)2 integrale generale, y = 1 integrale singolareSol. es. 7.16 — y(x) = 8 + C(x − 4)e − 4x − 4Sol. es. 7.17 — y 2 (2y + 1) = −x cos (x) + sin (x) + CSol. es. 7.18 — y(x) = Ce 3x+x2 /2 − 162