Question

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 1

Answer:

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

Step-by-step explanation:

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

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

        = $\frac{1}{4}\frac{d}{dx} (x^5) + C\frac{d}{dx} (x^{-3} )$

        = $\frac{5}{4} x^4 - 3Cx^{-4}$

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