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

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

Step-by-step explanation:

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

        =

        =

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

1

x = 1

step-by-step explanation:

0 ÷ x = 0

0 ÷ 1 = 0

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.