Question-128667

Question Number 128667 by sarahvalencia last updated on 09/Jan/21

Commented by liberty last updated on 09/Jan/21

(1) a^{2} da + 2 ab db + b^{2} da = 0

d ({ab}^{2}) + a^{2} da = 0

\int d ({ab}^{2}) + \int a^{2} da = \int 0 da

{ab}^{2} + \frac{1}{3} a^{3} = C

Answered by mohammad17 last updated on 09/Jan/21

1) M = a^{2} + b^{2} \to M_{b} = 2 b, N = 2 a b \to N_{a} = 2 b

M_{b} = N_{a} = 2 b \Rightarrow T h e e q u a t i o n i s e x a c t

\int M d a + \int N d b = C

\int (a^{2} + b^{2}) d a + \int 2 a b d b = C

\frac{a^{3}}{3} + 2 {a b}^{2} = C

⊝ m o h a m m a d

Commented by liberty last updated on 09/Jan/21

d (\frac{a^{3}}{3} + {2 ab}^{2}) = 0

a^{2} da + 4 ab db + {2 b}^{2} da = 0

wrong .

Answered by mohammad17 last updated on 09/Jan/21

2) b y s e p r a p l e

\int d x + \int \frac{n}{5 n^{2} - y} d y = C

x - n l n ∣ 5 n^{2} - y ∣= C

⊛ m o h a m m a d