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Question Number 101558 by mhmd last updated on 03/Jul/20

if y=sin2x is the solution of differintial equation   (d^2 y/dx^2 ) +4y=k then the k is .......

$${if}\:{y}={sin}\mathrm{2}{x}\:{is}\:{the}\:{solution}\:{of}\:{differintial}\:{equation}\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\mathrm{4}{y}={k}\:{then}\:{the}\:{k}\:{is}\:....... \\ $$

Answered by bemath last updated on 03/Jul/20

y′=2cos 2x ⇒y′′=−4sin 2x  y′′+4y=−4sin 2x+4sin 2x = 0 = k ★

$$\mathrm{y}'=\mathrm{2cos}\:\mathrm{2x}\:\Rightarrow\mathrm{y}''=−\mathrm{4sin}\:\mathrm{2x} \\ $$$$\mathrm{y}''+\mathrm{4y}=−\mathrm{4sin}\:\mathrm{2x}+\mathrm{4sin}\:\mathrm{2x}\:=\:\mathrm{0}\:=\:\mathrm{k}\:\bigstar \\ $$

Commented by mhmd last updated on 03/Jul/20

thank you sir

$${thank}\:{you}\:{sir} \\ $$

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