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

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

Explanation:

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

`y' (x ) = (d)/(dx) ((1)/(4) x^5 +Cx^(-3) )`

=
`(1)/(4)(d)/(dx) (x^5) + C(d)/(dx) (x^(-3) )`

=
`(5)/(4) x^4 - 3Cx^(-4)`

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