Which of the options is the differential equation that accepts the solution of the following equation? y(x)=c_{1}\cos x+c_{2}\sin x y''+y=0 y''+y'=0 y''-y=0 y''-y'=0 y''+y'-y=0

nitraiddQ

nitraiddQ

Answered question

2021-05-04

Which of the options is the differential equation that accepts the solution of the following equation?
y(x)=c1cosx+c2sinx
y+y=0
y+y=0

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-05-05Added 105 answers

Step 1
y(x)=c1cos(x)+c2sin(x)...(i)
y=c1sin(x)+c2cos(x)...(ii)
y=c1cos(x)c2sin(x)...(iii)
Step 2
y=(c1cos(x)+c2sin(x))
y''=-y by (i)
y''+y=0

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