Find the particular solution to the differential equation. (Remember to

vetrila10

vetrila10

Answered question

2021-12-04

Find the particular solution to the differential equation. (Remember to use absolute values where appropriate.)
dydx=x+1xy when x=1 , y=4

Answer & Explanation

Upout1940

Upout1940

Beginner2021-12-05Added 9 answers

Step 1
Given,
dydx=x+1xy, where x=1, y=4
Step 2
Now,
dydx=x+1xy
ydy=x+1xdx
Integrating both sides, we have
ydy=x+1xdx
y22=(x+1x)dx
y22=x22+ln|x|+C
Put x=1, y=4, then
(4)22=(1)22+ln|1|+C
8=12+C
812=C
C=152
The solution becomes :
y22=x22+ln|x|+152
y2=x2+2ln|x|+15
y=x2+2ln|x|+15
y=x2+2ln|x|+15

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