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A new tag was created by Hyperplane.
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Let $A\colon \mathbb R^n\to\mathbb R^{n\times n}$ be a matrix valued function, and $v, w\colon \mathbb R^n\to\mathbb R^n$ vector fields. I want to find a function/vector field $u\colon\mathbb R^n\to\mathbb R^n$ that satisfies $$u'(x) \cdot v(x) + A(x)\cdot u(x)=w(x)$$ for all $x$. Is this a k...

In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. Such systems occur as the general form of (systems of) differential equations for vector–valued functions x in one independent variable t, F ( x ˙ ( t ) , x ( t ) , t )...