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IV. Differentialligninger – 2. 1. ordens ligninger 330 1. Bestem en stamfunktion 2. Bestem en stamfunktion 3. Skriv løsningen A(x) = a(x)dx B(x) = e −A(x) b(x)dx y(x) = Ce A(x) + B(x)e A(x) 2.12. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 Angiv den fuldstændige løsning til differentialligningen y ′ + 2y = xe −2x + 3 Angiv endvidere den partikulære løsning y(x), der opfylder y(0) = 2. Løsning giver y ′ = −2y + (xe −2x + 3) a(x) = −2,b(x) = xe −2x + 3
IV. Differentialligninger – 2. 1. ordens ligninger 331 2.13. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 - fortsat A(x) = a(x)dx = −2dx = −2x B(x) = e −A(x) b(x)dx = e 2x (xe −2x + 3)dx Som giver = 1 2 x2 + 3 2 e2x 2.14. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 - fortsat fuldstændig løsning y(x) = Ce A(x) + B(x)e A(x) = Ce −2x + ( 1 2 x2 + 3 2 e2x )e −2x = Ce −2x + 1 2 x2 e −2x + 3 2 2.15. Opgave ☞ Matematik Alfa 1, August 2002 Opgave 1 - fortsat
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CALCULUS "SLIDES" TIL CALCULUS 1 +
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3. Generelle områder 201 4. Koordi
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Forord "Slides" til forelæsningern
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V. Matricer - 4. Determinanter = (
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Litteratur • Arnold, Ordinary dif
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0-række/søjle, 423 n-te afsnitssu
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Identitetsmatricen, 383 Identitetsm
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