Jawaban:

Contoh :

Carilah penyelesaian umum PD, (4x ^ 3 + x ^ 2 - y ^ 2) * dx + 2xydy = 0

Jawab PD Eksak or Non eksak

M = 4x ^ 3 + x ^ 2 - y ^ 2, N = 2xy

-2y, ду

ax = 2y =

= ay ax -4y, p= Faktor Integrasi u ay ax N -4y! 2xy!

u = e ^ (- integrate 2/x dx) = e ^ (- 2 * ln(x))

= e ^ ln(1/(x ^ 2)) = 1/(x ^ 2) .

PD menjadi,

1/(x ^ 2) * (4x ^ 3 + x ^ 2 - y ^ 2) * dx + 1/(x ^ 2) * (2xydy) = 0

dx+ 2y X =

PD Eksak,

Solusi PD Eksak, F(x,y) = c, dimana :

F(x, y) = integrate (4x + 1 - (y ^ 2)/(x ^ 2)) dx + g(y)

= 2x ^ 2 + x + (y ^ 2)/x +g(y) Rightarrow g(y)=c.

Solusi.

2x ^ 3 + x ^ 2 + y ^ 2 = cx