First Order Differential equation with complex coefficients: $y' + dfrac{1}{x+i}y = 0$
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I'm looking for a way to solve this differential equation with complex numbers. $$(E) : y' + dfrac{1}{x+i}y = 0$$
The professor expects a solution over the real numbers. He suggests to first split $dfrac{1}{x+i}$ into its real and imaginary part, which I did. I fail to see what to do next. Should I only solve $(E)$ for the real part of that number?
Thank you in advance.
differential-equations
asked Dec 5 at 9:53
DeltaXY
152
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up vote
1
down vote
favorite
I'm looking for a way to solve this differential equation with complex numbers. $$(E) : y' + dfrac{1}{x+i}y = 0$$
The professor expects a solution over the real numbers. He suggests to first split $dfrac{1}{x+i}$ into its real and imaginary part, which I did. I fail to see what to do next. Should I only solve $(E)$ for the real part of that number?
Thank you in advance.
differential-equations
asked Dec 5 at 9:53
DeltaXY
152
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm looking for a way to solve this differential equation with complex numbers. $$(E) : y' + dfrac{1}{x+i}y = 0$$
The professor expects a solution over the real numbers. He suggests to first split $dfrac{1}{x+i}$ into its real and imaginary part, which I did. I fail to see what to do next. Should I only solve $(E)$ for the real part of that number?
Thank you in advance.
differential-equations
asked Dec 5 at 9:53
DeltaXY
152
I'm looking for a way to solve this differential equation with complex numbers. $$(E) : y' + dfrac{1}{x+i}y = 0$$
The professor expects a solution over the real numbers. He suggests to first split $dfrac{1}{x+i}$ into its real and imaginary part, which I did. I fail to see what to do next. Should I only solve $(E)$ for the real part of that number?
Thank you in advance.
differential-equations
differential-equations
asked Dec 5 at 9:53
DeltaXY
152
asked Dec 5 at 9:53
DeltaXY
152
asked Dec 5 at 9:53
DeltaXY
152
asked Dec 5 at 9:53
DeltaXY
152
asked Dec 5 at 9:53
DeltaXY
152
152
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add a comment |
1 Answer
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How about multiplying by $x+i$ to get
$$left[(x+i) y right]'=(x+i)y'+y=0? $$
answered Dec 5 at 10:02
user1337
17k43291
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1 Answer
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1 Answer
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active
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active
oldest
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active
oldest
votes
up vote
2
down vote
accepted
How about multiplying by $x+i$ to get
$$left[(x+i) y right]'=(x+i)y'+y=0? $$
answered Dec 5 at 10:02
user1337
17k43291
add a comment |
up vote
2
down vote
accepted
How about multiplying by $x+i$ to get
$$left[(x+i) y right]'=(x+i)y'+y=0? $$
answered Dec 5 at 10:02
user1337
17k43291
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
How about multiplying by $x+i$ to get
$$left[(x+i) y right]'=(x+i)y'+y=0? $$
answered Dec 5 at 10:02
user1337
17k43291
How about multiplying by $x+i$ to get
$$left[(x+i) y right]'=(x+i)y'+y=0? $$
answered Dec 5 at 10:02
user1337
17k43291
answered Dec 5 at 10:02
user1337
17k43291
answered Dec 5 at 10:02
user1337
17k43291
answered Dec 5 at 10:02
user1337
17k43291
17k43291
add a comment |
add a comment |
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