n F(x,y,y,,y(n))=0 F(x,y,y,,y(n)) x,y,y, n- , F y(n).
, y(n)=f(x), f(x) .
n- : y=(x,C1,C2,,Cn), n : F(x,y,y,,y(n))=0 .
, C1,C2,,Cn, .
: y=(C21+2C2+C3)x+C4+6C5 2- ђ=C21+2C2+C3 ђ=C4+6C5 y=Cx+C
, 2- , F(x,y,y,y)=0
, 1- .
1. y, .. F(x,y,y)=0
z, y=z. y=z =>
F(x,z,z)=0 .. z.
z=(x,C1), y=(x,C1), y=S(x,1)dx+2
, , .
2. x, .. F(y,y,y)=0
. . , : . , . , ( ).
. : .
, :
: , , : . , .
3. y=z(dz/dy), z=yx
, y,y,y, , . ,
A(x)y(n)+B(x)y(n-1)++K(x)y+L(x)y=M(x) A(x), B(x)K(x), L(x), M(x) , A(x) 0 A(x), y(n)+b(x)y(n-1)+..+k(x)y+l(x)y=m(x), b(x)=B(x)/A(x),..,m(x)=M(x)/A(x)
m(x) . m(x)=0, . m(x) 0, , A(x), B(x)K(x), L(x) , .
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