Solve the following differential equation

given Y(0) = 4

To solve the given second-order linear homogeneous differential equation, let's denote \(y\) as the dependent variable and \(x\) as the independent variable. The given differential equation is:

\[
\frac{d^2y}{dx^2}\frac{dy}{dx} + 10y = 2
\]

This is a second-order linear differential equation. To solve it, we'll use the following standard method. Let \(v = \frac{dy}{dx}\), then the given equation becomes a first-order differential equation:

\[
v\frac{dv}{dx} + 10y = 2
\]

Now, let's solve this equation.

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