@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-D1Z5GPBM-Z
  skos:prefLabel "équation différentielle"@fr, "differential equation"@en ;
  a skos:Concept ;
  skos:narrower psr:-VLW2WCS1-L .

psr:-VLW2WCS1-L
  skos:definition """Une équation différentielle linéaire est un cas particulier d'équation différentielle pour lequel on peut appliquer des procédés de superposition de solutions, et exploiter des résultats d'algèbre linéaire. De nombreuses équations différentielles de la physique vérifient la propriété de linéarité. De plus, les équations différentielles linéaires apparaissent naturellement en perturbant une équation différentielle (non linéaire) autour d'une de ses solutions. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/%C3%89quation_diff%C3%A9rentielle_lin%C3%A9aire">https://fr.wikipedia.org/wiki/%C3%89quation_diff%C3%A9rentielle_lin%C3%A9aire</a>)"""@fr, """In mathematics, a <b>linear differential equation</b> is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form  <div class="mwe-math-element"><div class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle a_{0}(x)y+a_{1}(x)y'+a_{2}(x)y''\\\\cdots +a_{n}(x)y^{(n)}=b(x)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>0</mn>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>         <mi>y</mi>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>1</mn>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>         <msup>           <mi>y</mi>           <mo>′</mo>         </msup>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>         <msup>           <mi>y</mi>           <mo>″</mo>         </msup>         <mo>⋯<!-- ⋯ --></mo>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msub>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mo stretchy="false">(</mo>             <mi>n</mi>             <mo stretchy="false">)</mo>           </mrow>         </msup>         <mo>=</mo>         <mi>b</mi>         <mo stretchy="false">(</mo>         <mi>x</mi>         <mo stretchy="false">)</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{0}(x)y+a_{1}(x)y'+a_{2}(x)y''\\\\cdots +a_{n}(x)y^{(n)}=b(x)}</annotation>   </semantics> </math></div><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8760cf055e70d4f2844a87221e4e4fd3933d957c" class="mwe-math-fallback-image-display mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:49.68ex; height:3.343ex;" alt="{\\\\displaystyle a_{0}(x)y+a_{1}(x)y'+a_{2}(x)y''\\\\cdots +a_{n}(x)y^{(n)}=b(x)}"></div> where <span class="nowrap"><span class="texhtml"><i>a</i><sub>0</sub>(<i>x</i>)</span>, ..., <span class="texhtml"><i>a</i><sub><i>n</i></sub>(<i>x</i>)</span></span> and <span class="texhtml"><i>b</i>(<i>x</i>)</span> are arbitrary differentiable functions that do not need to be linear, and <span class="texhtml"><i>y</i>′, ..., <i>y</i><sup>(<i>n</i>)</sup> </span> are the successive derivatives of an unknown function <span class="texhtml mvar" style="font-style:italic;">y</span> of the variable <span class="texhtml mvar" style="font-style:italic;">x</span>. Such an equation is an ordinary differential equation (ODE). A <i>linear differential equation</i> may also be a linear partial differential equation (PDE), if the unknown function depends on several variables, and the derivatives that appear in the equation are partial derivatives.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Linear_differential_equation">https://en.wikipedia.org/wiki/Linear_differential_equation</a>)"""@en ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Linear_differential_equation>, <https://fr.wikipedia.org/wiki/%C3%89quation_diff%C3%A9rentielle_lin%C3%A9aire> ;
  skos:broader psr:-D1Z5GPBM-Z ;
  skos:prefLabel "équation différentielle linéaire"@fr, "linear differential equation"@en ;
  skos:inScheme psr: ;
  a skos:Concept ;
  dc:modified "2024-10-18"^^xsd:date .