Find a general solution of the equation y''+y={x,0\leq x\leq . 1,1\leq x

facas9 2021-10-09 Answered

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 \(\displaystyle{y}{''}+{y}={\left\lbrace{x},{0}\leq{x}\leq.{1},{1}\leq{x}\right.}\) NoteNote that the solution is not differentiable at x = 1. (b) Find a particular solution of y''+y= \(x,0\leq x\leq 1.1,1\leq x \)that satises the initial conditions y(0)=0 and y′(0)=1.

 

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Expert Answer

delilnaT
Answered 2021-10-10 Author has 7103 answers
a)\(\displaystyle{y}={\left\lbrace{c}{1}{\cos{{x}}}+{c}_{{{2}}}{\sin{{x}}}+{x},{0}\leq{x}\leq{1}.{c}_{{{1}}}{\cos{{x}}}+{c}_{{{2}}}{\sin{{x}}}+{1},{x}\geq{1}\right.}\)
b)\(\displaystyle{y}={\left\lbrace{x},{0}\leq{x}\leq{1.1},{x}\leq{1}\right.}\)
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