Verify y=x \tan x is solution to ODE: xy'=y+x^2+y^2 Verify Sy

Kymani Shepherd

Kymani Shepherd

Answered question

2022-04-21

Verify y=xtanx is solution to ODE: xy=y+x2+y2
Verify Sy=xtan{x}
is a solution to xy=y+x2+y2

Answer & Explanation

jeffster830gyz

jeffster830gyz

Beginner2022-04-22Added 21 answers

Step 1
y=xtan(x).
Verify that xy'=y+x2+y2.
Step 2
Alternate approach:
ddxtan(x)=sec2(x).
tan2(x)+1=sec2(x).
LHS equals:
x[xsec2(x)+tan(x)]=x2[tan2(x)+1]+y
=x2tan2(x)+x2+y=y2+x2+y.

elvis0217t2x

elvis0217t2x

Beginner2022-04-23Added 13 answers

y'=tanx+x1cos2xy'=tanx+xcos2x+sin2xcos2xy'=tanx+x+xtan2xy'=y/x+x+y2/xxy'=y+x2+y2

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