Make and solve the given equation x dx + y dy=a2x dy − y dxx2 + y2

Name: Make and solve the given equation x dx + y dy=a2x dy − y dxx2 + y2
Uploaded: 2022-02-23T17:22:57+00:00
Description: Make and solve the given equation x dx + y dy=a2x dy − y dxx2 + y2

Question

Make and solve the given equation x dx + y dy=a2x dy − y dxx2 + y2

Corben Pittman · Accepted Answer

Given:x dx + y dy=a2x dy − y dxx2 + y2  x dx + y dy=a2(x dy − y dxx2 + y2)  =a2[x dy − y dxx2x2 + y2x2]  =a2[d(yx)1 + y2x2]  =a2[d(yx)1 + (yx)2]  ⇒ ∫ xdx + ∫ ydy=a2 ∫ [d(yx)1 + (yx)2] + C where C is a constant  ⇒ x22 + y22=a2 tan−1⁡(yx) C [sin⁡ ce ∫ dxx2 + a2=1a2 tan−1⁡xa + c]  Hence the solution of the given differential equation is x2 + y2=2a2tan−1⁡(yx)

Make and solve the given equation x dx + y dy=a2x dy − y dxx2

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