Find a particular solution

$y$ Subscript $pyp$

$of$ the following equation. Primes denote the derivatives with respect $tox.$

$y$ Superscript left parenthesis $5$ right parenthesis Baseline plus $2y$ Superscript left parenthesis $3$ right parenthesis Baseline plus $2y$ double prime equals $7x$ squared minus $7y(5)+2y(3)+2y=7x2-7$

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Part $1$

The particular solution $is$

$y$ Subscript $pyp(x)equals=$StartFraction $7$ Over $24$ EndFraction $x$ Superscript $4$ Baseline minus seven sixths $x$ cubed$724x4-76x3.$

Find a particular solution $y_{p}of$ the following equation. Primes denote the derivatives with respect $tox.$

$y^{(5)}+2y^{(3)}+2y^{\text{'}\text{'}}=7x^2-7$

The particular solution $is{y}_p(x)=,.$