Question

Solve....
dy/dx = x + y​

Answer 1

Answer:

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