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

Find the general solution of x,dy-y,dx=sqrt(x2+y2),dx for x>0.

  1. y + x2 + y2 = C x
  2. y - x2 + y2 = C x2
  3. y + x2 + y2 = C
  4. y + x2 + y2 = C x2

Answer

D. y + x2 + y2 = C x2

Solution

For x>0: dy/dx= yx+ sqrt(x2+y2)x. With y=vx: xv'=sqrt(1+v2) dvsqrt(1+v2)=dx/x -1v= x+c v+sqrt(1+v2)=Cx, i.e. y+sqrt(x2+y2)=Cx2.

More Homogeneous First-Order Equations questions

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

All Homogeneous First-Order Equations questions