Particular Integrals Quiz

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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 $F(D)y = X^α, α > 0$?

α > 0 Signup and view all the answers

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

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

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

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

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

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

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

When $α > 0$ Signup and view all the answers

What are the special cases for the particular integral?

Case 3: When $rX^α, α > 0$ Signup and view all the answers

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

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

Particular Integrals Quiz

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Questions and Answers

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

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

What is the general formula for the particular integral?

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

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

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

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

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

What are the special cases for the particular integral?

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

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