CHO BI^E'U THU.C

164)

Cho bi^e'u thu.c:

^{h(x)( 1}x+ydyx+y −ln(x+y))dx+ 1

Ha~y tm ham s^o

^h(x)

sao cho bi^e'u thu.c tr^en tro.' thanh vi ph^an toan ph^an cu'a

m^o.t ham

^{F(x, y)}

va tm ham s^o do.

HD gia’i:

D - a.t

^{P =h(x)}_x+¹ _y^{ln (x+y)}Q=h(x). 1x+y

(D - i^eu ki^e.n x+y > 0) d^e'

^{P dx+Qdy}

la vi ph^an toan ph^an:

∂P∂y = ∂Q∂x ⇔ −h(x)(x+y+ 1)(x+y)

²

= h

⁰

(x)(x+y)−h(x)(x+y)

²

⇔h

⁰

(x+y) +h(x+y) = 0⇔h

⁰

+h= 0 ⇔h(x) = e

^−x

Va

^{F(x, y) =e}

^−x

^ln(x+y)