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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
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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