# In many physical applications, the nonhomogeneous term F(x) is specified by different formulas in different intervals of x. (a) Find a general solutio

In many physical applications, the nonhomogeneous term F(x) is specified by different formulas in different intervals of x. (a) Find a general solution of the equation $y+y=\left\{x,0\le x\le 1,1\le x\right\}$ NoteNote that the solution is not differentiable at x = 1. (b) Find a particular solution of $y+y=\left\{x,0\le x\le 1;1,1\le x\right\}$ that satises the initial conditions y(0)=0 and y′(0)=1.

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a)$y=\left\{c1\mathrm{cos}x+{c}_{2}\mathrm{sin}x+x,0\le x\le 1;{c}_{1}\mathrm{cos}x+{c}_{2}\mathrm{sin}x+1,x\ge 1$
b)$y=\left\{x,0\le x\le 1;1,x\le 1$