query: Why is the solution of an ordinary differential equation required to be defined on an interval?
positive_passages.docid: 86407
positive_passages.text: Why is it differential equations exist on an interval instead of a domain?
negative_passages.docid: 149794
negative_passages.text: Differential equation with resonance
negative_passages.docid: 71465
negative_passages.text: solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
negative_passages.docid: 54250
negative_passages.text: To solve the non linear IVP $y'(t)=1-y^2(t)$
negative_passages.docid: 46357
negative_passages.text: DSolve not finding solution I expected
negative_passages.docid: 136692
negative_passages.text: Why should the spatial derivative order of the ODE *not* exceed two?
negative_passages.docid: 82488
negative_passages.text: Periodic solution of differential equation $y′=f(y)$
negative_passages.docid: 121902
negative_passages.text: Using the Existence and uniqueness theorem to find the interval of validity of a unique solution in a Linear ODE
negative_passages.docid: 138742
negative_passages.text: Why must the integral of a nonzero continuous function be nonzero?
negative_passages.docid: 72604
negative_passages.text: The differential equation $y''-q(x)y=0.$
negative_passages.docid: 125233
negative_passages.text: Why is an open interval not a compact set?
negative_passages.docid: 30697
negative_passages.text: Solution of a Riccati ODE
negative_passages.docid: 100283
negative_passages.text: How to understand the notion of a differential of a function
negative_passages.docid: 131197
negative_passages.text: solution of a ODE with a function of $\dot{x}$
negative_passages.docid: 107620
negative_passages.text: Determining stability of the differential equation
negative_passages.docid: 69911
negative_passages.text: Does non-uniqueness of solution to 1st order ODE implies the existence of infinitely many solutions?
negative_passages.docid: 152143
negative_passages.text: Limits for the solution of the non-linear ODE