# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### Confusing differential equation $y+\frac{dy}{dx}=5x$ [closed]

How do I solve this differential equation for $y$? $$y+\frac{dy}{dx}=5x$$ What does the one extra $y$ with $\frac{dy}{dx}$ mean and is it linear?
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### General solution to linear differential equation with complex coefficients

I have a homogeneuous, linear differential equation with constant but complex coefficients: $$\frac{d^2y}{dx^2}-(a+\boldsymbol{i}b)y=0, (1)$$ where $\boldsymbol{i}$ is a imaginary unit. I do know ...
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### Is there a way to decide whether a differential equation is solvable or not?

Martin Davis, Yuri Matiyasevich, Hilary Putnam and Julia Robinson had negatively settled Hilbert 10th problem, I wonder if there is an analog result to the differential equations ?
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### Find all solutions of the IVP $ty' = y$, $y(t_0) = y_0$

Consider the IVP $ty' = y$, $y(t_0) = y_0$. Find all pairs $(t_0,y_0)$ such that the equation has: a) no solution b) a unique solution So I know that by the uniqueness theorem, since $g(t)=0$ is ...
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### order of numerical approximation of differential equation, when solution is not one-dimensional

In Wikipedia https://en.wikipedia.org/wiki/Numerical_methods_for_ordinary_differential_equations, differential equation's $y(t)$ is $\mathbb{R}^d$. However, when describing order of the numerical ...
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### Does the general solution of a second-order-non-homogeneous-linear-differential equation with complex roots count as a cosine/sine term? [closed]

Say a second ODE $D(x) = Acos(Bx)$ has the general solution $C_1e^{\alpha ix} + C_2e^{\beta ix}$ where $\alpha i$ and $\beta i$ are the complex roots of the auxiliary equation of $D(x)$; Then, does ...
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### Differential Equations: Jordan Form of a Matrix

I am using Lawrence Perko's book Differential Equations and Dynamical Systems, for my Differential Equations course. At the moment we are going over Jordan Forms of a linear system $x^{'}(t) = Ax$, ...
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### Autonomous exponentially stable steady-state and small non-vanishing perturbations

My question considers if an autonomous system having a exponentially stable steady-state will continue to do so for non-vanishing small perturbations. Consider the system ...
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### Can an ODE be linear and separable?

In my introductory differential class, the professor stated that there exist some ODEs that are both linear and separable. I'm a bit confused, because I was under the impression that a separable ...
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### solving ODE : $xy'=$sin$(x+y)$

May I ask some hints or solution for solving $xy'=$sin$(x+y)$?? My idea was substitution : $x+y=u$, then it becomes $x(u'-1)=$sin$u$ and still I can't approach further..
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### Strange differential eqn

I've a strange question here which I don't really understand. I've been asked to solve for $f(x)$: $f '(x) + af(x) = bg(x) + ch(x) +dl(x)$ And I don't understand how I'm supposed to get that in ...
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### Help solving autonomous, non-linear ODE

Apologies if this is a very basic question - it's many years since I've done any calculus. I have a differential equation of the form $$\frac{dy(t)}{dt} = e^{-y(t)} - 1 - y(t)$$ I think this has an ...