Question

Solve dy/dx+xy=x. Differential equation.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

How can I solve dy/dx=x-y/x+y?

dydx=x−yx+y

Put,y=vx

⟹dydx=v+xdvdx

⟹v+xdvdx=1−v1+v

⟹xdvdx=1−2v−v21+v

⟹∫v+1(v+1)2−2dv=−∫1xdx

⟹12ln|(v+1)2−2|=−ln|x|+ln|c1|

⟹ln|[(v+1)2−2]|=2ln∣∣c1x∣∣

⟹x2(v2+2v−1)=C

WhereC=2ln|c1|

Since,v=yx

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

OnePlus 7T.

dy/dx=x-y/x+y

Let y=vx

dy/dx=xdv/dx+v

xdv/dx+v=(x-vx) /(x+vx)

=(1-v)/(1+v)

xdv/dx=(1-v)/(1+v)-v

xdv/dx=(1-v-v-v^2)/1+v

(1+v)dv/(1–2v-v^2)=dx/x

put 1–2v-v^2=t

-2(1+v)dv=dt

-dt/2t=dx/x

Integrating both side

-1/2lnt=lnx+lnc

lnt^-1/2=lnxc

1/√t=xc

1/√1–2v-v^2)=xc

1/√1–2y/x-(y/x)^2=xc

x/√x^2–2yx-y^2=xc

√x^2-y^2–2yx=1/c