Solve the following differential equation. As you know, indefinite integrals are used to solve these equations and have an undetermined constant. In this exercise use $C=0$.
$\displaystyle\frac{\hbox{d}y}{\hbox{d}x} + 2y = x$
$y =$

Use the formula: $$\int x e^{2x} \hbox{d} x = e^{2x} \left(\frac{x}{2} - \frac{1}{4}\right).$$ Of course, you can check that formula easily by differentiation. (Also, check your solution of the differential equation by differentiation.)
Hint: Recognize this as a first-order linear differential equation and follow the general method for solving these.