esbagoar7kh

2022-04-24

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

Expert

Explanation:
From your equation it follows that

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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