Question

Решить дифференциальное уравнение: y'=2((y+2)/(x+y-1))^2

Answer 1

( dy/dx ) ( 2x – y ) = x + 2y ;( 2x – y ) dy = ( x + 2y ) dx ;( 2x – y ) d( x * y/x ) = ( x + 2y ) dx ;( 2 – y/x ) d( x * y/x ) = ( 1 + 2y/x ) dx ;( 2 – y/x ) ( x d(y/x) + y/x dx ) = ( 1 + 2y/x ) dx ;2x d(y/x) + 2 (y/x) dx – x (y/x) d(y/x) – ((y/x)^2) dx = dx + 2 ( y/x ) dx ;2x d(y/x) – x (y/x) d(y/x) – ((y/x)^2) dx = dx ;2x d(y/x) – x (y/x) d(y/x) = dx + ((y/x)^2) dx ;x ( 2 – y/x ) d(y/x) = ( 1 + ((y/x)^2) ) dx ;( 2 – y/x ) d(y/x) / ( 1 + ((y/x)^2) ) = dx / x ;2 d(y/x) / ( 1 + ((y/x)^2) ) – y/x d(y/x) / ( 1 + ((y/x)^2) ) = dx / x ;4 d(y/x) / ( 1 + ((y/x)^2) ) = d(y/x)^2 / ( 1 + ((y/x)^2) ) + 2 dx / x ;4 d(y/x) / ( 1 + ((y/x)^2) ) = d( 1 + (y/x)^2 ) / ( 1 + ((y/x)^2) ) + 2 dx / x ;