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Further Maths: Core Pure -Edexcel-A Level

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  1. complex-numbers-and-argand-diagrams
    6 主题
  2. exponential-form-and-de-moivres-theorem
    4 主题
  3. properties-of-matrices
    3 主题
  4. transformations-using-matrices
    3 主题
  5. roots-of-polynomials
    2 主题
  6. series
    2 主题
  7. maclaurin-series
    1 主题
  8. hyperbolic-functions
    4 主题
  9. volumes-of-revolution
    2 主题
  10. methods-in-calculus
    5 主题
  11. vector-lines
    4 主题
  12. vector-planes
    4 主题
  13. polar-coordinates
    2 主题
  14. first-order-differential-equations
    3 主题
  15. second-order-differential-equations
    2 主题
  16. simple-harmonic-motion
    2 主题
  17. proof-by-induction
    2 主题
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First order differential equations

What is a differential equation?

  • A differential equation is simply an equation that contains derivatives

    • For example fraction numerator straight d y over denominator straight d x end fraction equals 12 x y squared is a differential equation

    • And so is fraction numerator straight d squared x over denominator straight d t squared end fraction minus 5 fraction numerator straight d x over denominator straight d t end fraction plus 7 x equals 5 sin invisible function application t

What is a first order differential equation?

  • A first order differential equation is a differential equation that contains first derivatives but no second (or higher) derivatives

    • For example fraction numerator straight d y over denominator straight d x end fraction equals 12 x y squared is a first order differential equation

    • But <img alt=”fraction numerator straight d squared x over denominator straight d t squared end fraction minus 5 fraction numerator straight d x over denominator straight d t end fraction plus 7 x equals 5 sin invisible function application t” data-mathml='<math ><semantics><mrow><mfrac><mrow><msup><mi mathvariant=”normal”>d</mi><mn>2</mn></msup><mi>x</mi></mrow><mrow><mi mathvariant=”normal”>d</mi><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac><mo>-</mo><mn>5</mn><mfrac><mrow><mi mathvariant=”normal”>d</mi><mi>x</mi></mrow><mrow><mi mathvariant=”normal”>d</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mn>7</mn><mi>x</mi><mo>=</mo><mn>5</mn><mi>sin</mi><mo>⁡</mo><mi>t</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”49″ role=”math” 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