crepevine - ECD Germany
y^WORDYXxY.
May 02, 2026
y^WORDYXxY.
m*=ym=10y-=my=-8y+=yy=-16
y''+y=0 ==>y''=-y ==>y'dy'=-ydy ==>y'^2=C1^2-y^2 (C1) ==>y'= (C1^2-y^2) ==>dy/ (C1^2-y^2)=dx ==>arcsin (y/C1)=C2x (C2) ==>y ...
Understanding the Context
y=xty'=xt'+t xt'+t=t/ (t-1) ==>xt'=t (2-t)/ (t-1) ==> (t-1)dt/ [t (2-t)]=dx/x ==> [1/ (2-t)-1/t]dt=2dx/x ==>lnt-2+lnt=-2lnx+lnC (C) ==>t (t-2)=C/x.
y'= (xe^y)' y'=1e^y+xe^yy' y' (1-xe^y)=e^y y'=e^y/ (1-xe^y) y=1+xe^y1-xe^y=2-yy'=e^y/ (2-y) dy/dx=e^y/ (2-y) dy/dx=e^y/ (2-y) d (dy/dx)/dx=d (e^y/ (2-y)) d (dy/dx)/dx=.
sin (x+ y) cos (x + y) cos (x + y) = cos (x) * cos (y) - sin (x) * sin (y) .
yyy=8/15 (2x+C1)^ (5/2)+C2x+C3
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Key Insights
jqxy jqxy jqxyu jqxyn.
(3x+y+2) (3x-y-2) .
y + = y - = m * = y m = m * y 5 * 2 = 10; //m10 y = y - m 2 - 10 = -8; //y2-8 y = y + y -8 + -8 = -16; .
