Find the general solution of the given differential equation x\frac{dy}{dx}-y=x^2\sin x give

Linda Seales 2021-12-13 Answered
Find the general solution of the given differential equation
xdydxy=x2sinx
give the largest interval over which the genreral solution is defined.
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

Bernard Lacey
Answered 2021-12-14 Author has 30 answers
xdydxy=x2sinx
dydxyx=xsinx
This is 1-st order linear in y so integrating Factor =e1xdx
=eln(1x)
=1x
multiplying the given equation with I.F. we get
1xdydxyx2=sinx
ddx(yx)=sinx
integrating both side we get
d(yx)=sinx
yx=cosx+C
y=xcosx+Cx
Since y is continuous on (,) so longest inter val of existence is (,)
Since xcosx and Cx both does not goes to 0 as x
Hence then is no transient form.

We have step-by-step solutions for your answer!

Ella Williams
Answered 2021-12-15 Author has 28 answers
This will be useful to me. Thanks to.

We have step-by-step solutions for your answer!

Expert Community at Your Service

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

New questions