Bernoulli ODE: $y^\prime+a(x)y=b(x)y^n$
Why we need continuity of $a$ and $b$ on the interval we are working on?
For Bernoulli ODE $y^\prime+a(x)y=b(x)y^n$, why $a$ and $b$ are continuous?
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ordinary-differential-equations
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0To be pedantic, you're wondering why we require $a$ and $b$ are continuous. $a(x)$ and $b(x)$ are just numbers. – 2017-02-01
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0That is exactly what i m wondering – 2017-02-01
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0@Aweygan,are $a(x)$,$b(x)$ numbers? – 2017-02-01
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0@haqnatural Presumably. Unless andii is asking about a family of Bernoulli ODEs – 2017-02-01
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3When functions $a(x)$ and $b(x)$ are continues, the existence and uniqueness theorem ensures that one solution exactly exist. – 2017-02-01