Menu Close

convert-this-D-E-to-exact-D-E-and-solve-it-ydx-x-1-y-dy-0-




Question Number 169549 by ali009 last updated on 02/May/22
convert this D.E to exact D.E and solve it  ydx+x(1+y)dy=0
convertthisD.EtoexactD.Eandsolveitydx+x(1+y)dy=0
Answered by aleks041103 last updated on 02/May/22
y+x(1+y)(dy/dx)=0  ⇒(1+y)(dy/dx)=−(y/x)  ⇒((1+y)/y)dy=−(dx/x)  ∫((1+y)/y)dy=y+ln(y)+C  ∫−(dx/x)=−ln(x)  ⇒y+ln(y)+ln(x)=C  ye^y =(c/x)  ⇒y(x)=W((c/x))
y+x(1+y)dydx=0(1+y)dydx=yx1+yydy=dxx1+yydy=y+ln(y)+Cdxx=ln(x)y+ln(y)+ln(x)=Cyey=cxy(x)=W(cx)
Commented by ali009 last updated on 02/May/22
well done
welldone

Leave a Reply

Your email address will not be published. Required fields are marked *