Question

ADVANCED QUESTION !!!!

Solve ⤵️

$\frac{ {d}^{2}y }{d {x}^{2} } + 4y = 0$

Answer 1

$\huge\bigstar\underline\red{SOLUTION :-}$

GIVEN

$\frac{ {d}^{2}y }{d {x}^{2} } + 4y = 0$

HERE,

The auxiliary equation will be

${m}^{2} + 4 = 0$

${m}^{2} = - 4$

$m = ±2i$

$m = 0±2i$

Hence,

The general solution of the given differential is

y = ${e}^{ax} [C_1 cosβx + C_2 sin βx]$

y = ${e}^{0×x} [C_1 cos2x + C_2 sin 2x]$

y = $[C_1 cos2x + C_2 sin 2x]$

Answer....

HOPE IT HELPS ♥

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\pink{Answer:-}}}}}$

$\star {\bold{\underline{\underline{Given \: in \:question :-}}}}$

➡$\huge\frac{ {d}^{2}y }{d {x}^{2} } + 4y =0$

${\bold{\underline{\underline{ Equation \: will \: be:-}}}}$

$\to\ m^2+4 = 0 \\ \\ \to\ m^2= -4 \\ \\ \to\ m =+_-2i \\ \\ \to\ m= 0+_-2i$

•Now, General solution of this differential is :-

$\to\ y = {e}^{ax}[ C_1cosβx + C_2cosβx ] \\ \\ \to\ y = {e}^{0 X x}[C_1cos2x + C_2cos2x] \\ \\ \to\ [C_1cos2x + C_2cos2x]$

$\mathbb\red{Thanks...}$