Non zero solution of y′(t)=f(x,t)y(t)One of the examples in my textbook mentions that y′(t)=f(x,t)y(t) has...





Non zero solution of y(t)=f(x,t)y(t)
One of the examples in my textbook mentions that y(t)=f(x,t)y(t) has nonzero solution if and only if f(x,t) does not depend on x. Why is this?

Answer & Explanation

Waylon Padilla

Waylon Padilla


2022-04-25Added 19 answers

From your equation it follows that
f(x,t)=y(t)y(t),(t, s.t.  y(t)0)
Where the r.h.s only depends on t, so naturally the l.h.s. must also be constant in x.

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