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First verify that y(x)y(x) satisfies the given differential equation. Then determine a value of the constant CC so that y(x)y(x) satisfies the given initial condition. Use a computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition.
x dy/dx+3y=2x5; y(x)=1/4 x5+Cx−3,y(2)=1

Answer :

batolisis

Answer:

at constant C = -56 satisfies the given condition of y(x)

Step-by-step explanation:

differentiate y(x) w.r.t.x

[tex]y' (x ) = \frac{d}{dx} (\frac{1}{4} x^5 +Cx^{-3} )[/tex]

        = [tex]\frac{1}{4}\frac{d}{dx} (x^5) + C\frac{d}{dx} (x^{-3} )[/tex]

        = [tex]\frac{5}{4} x^4 - 3Cx^{-4}[/tex]

attached is the remaining part of the detailed solution and the sketch of the several typical solutions

${teks-lihat-gambar} batolisis
${teks-lihat-gambar} batolisis

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