The order of the differential equation whose general solution is … - Vidyadip

MCQ

The order of the differential equation whose general solution is given by $y = {C_1}{e^{2x + {C_2}}} + $ ${C_3}{e^x} + {C_4}\sin (x + {C_5})$ is

A
$5$
✓
$4$
C
$3$
D
$2$

✓

Answer

Correct option: B.

$4$

b
(b) $y = {C_1}{e^{2x + {C_2}}} + {C_3}{e^x} + {C_4}\sin (x + {C_5})$

$ = {C_1}.{e^{{C_2}}}{e^{2x}} + {C_3}{e^x} + {C_4}(\sin x\cos {C_5} + \cos x\sin {C_5})$

$ = A{e^{2x}} + {C_3}{e^x} + B\sin x + D\cos x$

Here, $A = {C_1}{e^{{C_2}}}$, $B = {C_4}\cos {C_5}$, $D = {C_4}\sin {C_5}$

(Since equation consists of four arbitrary constants)

order of differential equation $= 4.$

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