Particular Integrals Quiz
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Questions and Answers

What is the particular integral of the differential equation $D^2y/dx^2 + dy/dx = x^2 + 2x + 4$?

  • $2x^3/3 + 4x^2$
  • $x^3/3 + 4x$ (correct)
  • $x^2 + 2x + 4$
  • $3x^2 + 4x$

    • In which case is the particular integral of $F(D)y = X^α, α > 0$ given as $yp(x) = F(D)^{-1}X^α$?

  • Case 1
  • Case 3 (correct)
  • Case 2
  • Case 4

    • What is the general formula for the particular integral?

  • yp(x) = F(D)^{-1}X^α (correct)
  • yp(x) = F(D)X^α
  • yp(x) = F(D)X^α + X^β
  • yp(x) = F(D)^{-1}X^β

    • What should be the value of α for the particular integral of $F(D)y = X^α, α > 0$?

    <p>α &gt; 0</p> Signup and view all the answers

    How is the particular integral of $F(D)y = X^α, α > 0$ obtained?

    <p>By expanding $F(D)^{-1}$ as an infinite series in ascending powers of D and then operating on $X^α$</p> Signup and view all the answers

    What is the particular integral of the differential equation $D^2y/dx^2 + dy/dx = x^2 + 2x + 4$?

    <p>$x^3/3 + 4x$</p> Signup and view all the answers

    What is the formula for the particular integral when $F(D)y = X^α, α > 0$?

    <p>$yp(x) = F(D)^{-1}X^α$</p> Signup and view all the answers

    In which case is the particular integral of $F(D)y = X^α$ given as $yp(x) = F(D)^{-1}X^α$?

    <p>When $α &gt; 0$</p> Signup and view all the answers

    What are the special cases for the particular integral?

    <p>Case 3: When $rX^α, α &gt; 0$</p> Signup and view all the answers

    How is the particular integral of $F(D)y = X^α, α > 0$ obtained?

    <p>By expanding $F(D)^{-1}$ as an infinite series in ascending powers of $D$ and then operating on $X^α$</p> Signup and view all the answers

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