Engineering Board Exam Reviewer · Homogeneous First-Order Equations · medium

Find the general solution of x2dy/dx=y2+2xy.

1. y/x + y = C
2. y/x + y = C x
3. x/x + y = C y
4. y ≤ft(x + y ) = C x

Answer

B. y/x + y = C x

Solution

Let y=vx: v+xv'=v2+2v xv'=v2+v /v(v+1)=dx/x /v+1= x+c /v+1=Cx, i.e. y/x+y=Cx.

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