Question

Question ....dy/dx=x-y/x+y?


Answer... dydx=x−yx+ydydx=x−yx+y

Put,y=vxPut,y=vx

⟹dydx=v+xdvdx⟹dydx=v+xdvdx

⟹v+xdvdx=1−v1+v⟹v+xdvdx=1−v1+v

⟹xdvdx=1−2v−v21+v⟹xdvdx=1−2v−v21+v

⟹∫v+1(v+1)2−2dv=−∫1xdx⟹∫v+1(v+1)2− 2dv=−∫1xdx

⟹12ln|(v+1)2−2|=−ln|x|+ln|c1|. ⟹12ln⁡|(v+1)2−2|=−ln⁡|x|+ln⁡|c1|

⟹ln|[(v+1)2−2]|=2ln∣∣c1x∣∣⟹ln⁡|[(v+1)2−2]|=2ln⁡|c1x|

⟹(v+1)2−2=c21x2⟹(v+1)2−2=c12x2

⟹x2(v2+2v−1)=C⟹x2(v2+2v−1)=C

WhereC=c21WhereC=c12

Since,v=yxSince,v=yx

⟹y2+2xy−x2=CRequired General equation⟹y2+2xy−x2=C⏟Required General equation


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Answer 1

Answer:

sin cos

Step-by-step explanation:

sin cos is one of twh 2 y t 2yt