Solve differential equationdx/dy+x/y= 1/(sqrt(1+y^2))

aortiH

aortiH

Answered question

2020-11-27

Solve differential equation dxdy+xy=11+y2

Answer & Explanation

okomgcae

okomgcae

Skilled2020-11-28Added 93 answers

dxdy+p(y)x=q(y)
Compare the equation dxdy+p(y)x=q(y) to dxdy+xy=11+y2 and obtain p(y)=1y, q(y)=11+y2
I.F.=ep(y)dy
=elny
=y xep(y)dy=ep(y)dyq(y)dy+C
where C is arbitrary constant of equation
xep(y)dy=ep(y)dyq(y)dy+C
xy=y11+y2dy+C
xy=122y1+y2dy+C
xy=12(1+y2)1+y2dy+C [(1+y2)=2y]
xy=12(21+y2)+C [f(y)f(y)dy=2f(y)]
xy=1+y2+C
x=1+y2+Cy
x=1+y2y+Cy

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