I have a differential equation of the form d y <mrow class="MJX-TeXAtom-ORD"> /

gnatopoditw

gnatopoditw

Answered question

2022-06-21

I have a differential equation of the form
d y / d x + p ( x ) y = q ( x )
under the condition that q ( x ) = 300 if y < 3312 and q ( x ) = 0 if y 3312.
I could not understand how to solve this differential equation with such heavy side function ?
Any hints?

Answer & Explanation

Brendon Fernandez

Brendon Fernandez

Beginner2022-06-22Added 14 answers

Solve this equation on two domains separately: on ( , 3312 ) and on ( 3312 , + ), then use the arbitrary constant that you obtained in both cases to make y globally continuous.
Lucille Cummings

Lucille Cummings

Beginner2022-06-23Added 5 answers

MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document so you have the differential equation
d y d x + 2 40 + x y = k
multiplying by ( 40 + x ) 2 we get
math xmlns="http://www.w3.org/1998/Math/MathML" > k ( 40 + x ) 2 = ( 40 + x ) 2 d y d x + 2 ( 40 + x ) y = d d x ( ( 40 + x ) 2 y ) =
this gives
y = k 3 ( 40 + x ) + C ( 40 + x ) 2 .
for your problem we have
y = 100 ( 40 + x ) + C ( 40 + x ) 2  for  x 3312 y = D ( 40 + x ) 2  for  x 3312
the matching condition is
100 ( 40 + 3312 ) + C ( 40 + 3312 ) 2 = D ( 40 + 3312 ) 2

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?