query: Why is it correct to assume $f = e^{\lambda x}$ in differential equation?
positive_passages.docid: 27646
positive_passages.text: Why do we chose exponential function as a trial solution for second order linear differential equation with constant coefficient?
negative_passages.docid: 111669
negative_passages.text: How do lambda calculus most basic definitions work?
negative_passages.docid: 102013
negative_passages.text: The derivative of $e^x$ using the definition of derivative as a limit and the definition $e^x = \lim_{n\to\infty}(1+x/n)^n$, without L'Hôpital's rule
negative_passages.docid: 43430
negative_passages.text: What exactly does $\frac{dx}{dy}$ mean?
negative_passages.docid: 51817
negative_passages.text: Linear vs nonlinear differential equation
negative_passages.docid: 107572
negative_passages.text: How does the derivative with respect to the complex conjugate even make sense?
negative_passages.docid: 1641
negative_passages.text: Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
negative_passages.docid: 17754
negative_passages.text: Intuitive Understanding of the constant "$e$"
negative_passages.docid: 82448
negative_passages.text: Why is $f(x) = x\phi(x)$ one-to-one?
negative_passages.docid: 81784
negative_passages.text: Differential equation degree doubt
negative_passages.docid: 95123
negative_passages.text: General solution of expected value of E(f(X))?
negative_passages.docid: 155509
negative_passages.text: Does a linear operator obeying Leibniz rule imply it is a differential operator?
negative_passages.docid: 119380
negative_passages.text: Clarifying question on meaning of derivative of a linear transformation
negative_passages.docid: 92627
negative_passages.text: How do we know the Taylor expansion for $e^x$ works for all $x$? Or that it's analytic?
negative_passages.docid: 27812
negative_passages.text: Understanding the differential $dx$ when doing $u$-substitution
negative_passages.docid: 145136
negative_passages.text: When can we interchange the derivative with an expectation?
negative_passages.docid: 148355
negative_passages.text: Regarding Goldstein's claim that $\mathbf{F} = \dot{\mathbf{p}}$