Consider the differential equation dy dx = 2x 1+x^ 2 +4e^ 4x with the initial condition .

MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations

Problem

Consider the differential equation dydx=2x1+x2+4e4x\frac{dy}{dx}=\frac{2x}{1+x^{2}}+4e^{4x} with the initial condition y(0)=2y(0)=2. (a) Solve the differential equation to obtain the general expression for y(x)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 xx. (d) Determine y(ln⁡2)y(\ln 2). Express your answer exactly.

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