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

aortiH 2020-11-27 Answered

Solve differential equation dxdy+xy=11+y2

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

okomgcae
Answered 2020-11-28 Author has 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

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-11-26

Solve differential equation (x2lnx)y+xy=0

asked 2022-01-21

Convert the differential equation uu2u=e5t into a system of first order equations by letting x=u, y=u'
x=?
y=?

asked 2022-01-21
The equation y=yx(lnylnx+1) is?
1. First order, Partial.
2. First order, Non-homogenous.
3. None of above.
4. First order, Homogenous.
asked 2022-06-22
Construct an example of a first-order differential equation on R for which there are no solutions to any initial value problem.
Could anyone please get me started on this. I am struck as to which direction to go
asked 2022-01-21
Find the general solution of these first order differential equations
(1x)y=y2
asked 2022-06-22
Below is a problem I did. However, it did not match the back of the book. I would like to know where I went wrong.
Problem:
Solve the following differential equation.
y = y x x
Answer:
d y d x = y x x x = y x 1 y = x v d y d x = x d v d x + v x d v d x + v = v 1 x d v d x = 1 d v = d x x v = ln x + c y x = ln | x | + c y = x ln | x | + c x
The book's answer is:
y = x ln | k x |
Where did I go wrong?
asked 2022-02-16
y+eyx=0
that I have simplified like so
ey=xy
lney=ln(xy)
y=ln(xy)
but I do not know how to solve this further to obtain the general solution. I have done first order linear differential equation strategies so far. How should I get about doing this question with the strategies I have?