Differential Equations: Identifying homogenous or non homogenous functions. Show your complete

aspifsGak5u

aspifsGak5u

Answered question

2021-12-27

Differential Equations:
Identifying homogenous or non homogenous functions.
Show your complete solution.
when x=0,y=3
xydx(x+2)dy=0

Answer & Explanation

temnimam2

temnimam2

Beginner2021-12-28Added 36 answers

xydx(x+2)dy=0
xydx=(x+2)dy
xx+2dx=dy4
(x+22x+2)dx=dy4
((1)(2x+2)dx=dy4
Integrating both sides dx2x+2dx=dy4
x2ln|x+2|=m|y|+c
when x=0,4=3{given}
02ln(2)=ln3+cc=2ln(2)ln3
c=2(0.693)1.098
c=1.3861.098
c=0.484
x2ln|x+2|=ln|4|2.484
ln|4|=x2ln|x+2|+2.484
Serita Dewitt

Serita Dewitt

Beginner2021-12-29Added 41 answers

xydx(x+2)dy=0xydx=(x+2)dyx(x+2)dx=1ydy
x(x+2)dx=1ydy
x(x+2)dx=ln|y|+A
Use partial fractions to solve the remaining integral.
x(x+2)=A1+B(x+2)
x=A(x+2)+BA=1,2A+B=0A=1,B=(2)
x(x+2)=12(x+2)
Evaluate the new integrals
ln|y|+A=dx2(x+2)dx
ln|y|+A=x2ln|(x+2)|+B
Simplify the equation and then take exponentials.
ln|y|+2ln|(x+2)|=x+C
ln|y|+ln|(x+2)2|=x+C
ln|y(x+2)2|=x+C
y(x+2)2=Dex
Answer: y=Dex(x+2)2
karton

karton

Expert2022-01-10Added 613 answers

xydx(x+2)dy=0
xy(x+2)dydx=0
xy(x+2)y=0
Solve 1yy=xx+2
ln(y)=x+22ln(x+2)+c1
Isolate y: y=ex+2+c1x2+4x+4
Answer: y=ex+2+c1x2+4x+4

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