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

Find the general solution of dy/dx=y/x+ /x.

1. y/x = C x
2. y/x = C x
3. y/x = C
4. y/x = C x

Answer

B. y/x = C x

Solution

Let y=vx: v+xv'=v+ v v,dv=dx/x | v|= |x|+c yx=Cx.

More Homogeneous First-Order Equations questions

1. Find the general solution of (x2-y2),dx+2xy,dy=0.
2. Find the general solution of dy/dx=x2+y2/2xy.
3. Which substitution reduces a homogeneous first-order differential equation to a separable one?
4. Find the general solution of dy/dx=x+y/x for x>0.
5. Find the general solution of x,dy-y,dx=sqrt(x2+y2),dx for x>0.
6. Find the general solution of dy/dx=x+y/x-y.
7. Find the general solution of x2dy/dx=y2+2xy.

All Homogeneous First-Order Equations questions