\frac{dy}{dx}=y+1 Solving the above given differential equation, yields the following

Magdalena Norton 2022-05-02 Answered
dydx=y+1 Solving the above given differential equation, yields the following general solution. y+1=ex+C
y=Cex1
Solution y=1 at C=0
Can I say that y=1 is a singular solution?
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Answers (2)

timbreoizy
Answered 2022-05-03 Author has 15 answers
Step 1
y=1 is not a singular solution because it is included in the general solution y=Cex1 when C=0.
Solutions are only called singular when they are not attainable from the general solution form. In fact, I believe all linear first order homogenous equations have no singular solutions.
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Giancarlo Brooks
Answered 2022-05-04 Author has 11 answers
Step 1
y=1 is not a singular solution, because it does not pass by any point (x0, y0) such that the initial value problem
{y=y+1y(x0)=y0
has more than one solution: in point of fact, the Cauchy problem
{y=y+1y(x0)=1
has only the one maximal solution y=1, whatever x0 is.
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