Mathematics

Problem

Consider the differential equation

\frac{dy}{dx}=\frac{2x}{1+x^{2}}+4e^{4x}

with the initial condition

y(0)=2

. (a) Solve the differential equation to obtain the general expression for

y(x)

. (b) Use the initial condition to determine the particular solution. (c) Verify that your particular solution satisfies the differential equation for all real

x

. (d) Determine

y(\ln 2)

. Express your answer exactly.

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