this post was submitted on 18 Mar 2024
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Prompt: Suppose ϕ(t,y) is a function of two variables. A more general class of first order differential equations has the form y˙=ϕ(t,y). This is not necessarily a linear first order equation, since ϕ may depend on y in some complicated way; note however that y˙ appears in a very simple form. Under suitable conditions on the function ϕ, it can be shown that every such differential equation has a solution

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Image with seed 1812652324 generated via Stable Diffusion through @stablehorde@sigmoid.social. Prompt: Suppose ϕ(t,y) is a function of two variables. A more general class of first order differential equations has the form y˙=ϕ(t,y). This is not necessarily a linear first order equation, since ϕ may depend on y in some complicated way; note however that y˙ appears in a very simple form. Under suitable conditions on the function ϕ, it can be shown that every such differential equation has a solutionImage with seed 3829613452 generated via Stable Diffusion through @stablehorde@sigmoid.social. Prompt: Suppose ϕ(t,y) is a function of two variables. A more general class of first order differential equations has the form y˙=ϕ(t,y). This is not necessarily a linear first order equation, since ϕ may depend on y in some complicated way; note however that y˙ appears in a very simple form. Under suitable conditions on the function ϕ, it can be shown that every such differential equation has a solutionImage with seed 384382340 generated via Stable Diffusion through @stablehorde@sigmoid.social. Prompt: Suppose ϕ(t,y) is a function of two variables. A more general class of first order differential equations has the form y˙=ϕ(t,y). This is not necessarily a linear first order equation, since ϕ may depend on y in some complicated way; note however that y˙ appears in a very simple form. Under suitable conditions on the function ϕ, it can be shown that every such differential equation has a solution

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