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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The order of the differential whose general solution is given by ${\text{y}}=\text{C}_1\cos(2\text{x}+\text{C}_{2})+(\text{C}_{3}+\text{C}_{4})\text{a}^{\text{x}+\text{C}_{5}}+\text{C}_{6}\sin(\text{x}-\text{C}_{7}).$
  • A
    $3$
  • B
    $4$
  • ✓
    $5$
  • D
    $2$
✓

Answer

Correct option: C.
$5$
The given equation can be reduced to :
${\text{y}}=\text{C}_1\cos(2\text{x}+\text{C}_{2})+(\text{C}_{3}+\text{C}_{4})\text{a}^{\text{x}+\text{C}_{5}}+\text{C}_{6}\sin(\text{x}-\text{C}_{7})$
Where $\mathrm{C}=\mathrm{C}_3+\mathrm{C}_4$ be a constant
There are $5$ constant $\left(\mathrm{C}_1, \mathrm{C}_2, \mathrm{C}_3, \mathrm{C}_6, \mathrm{C}_7\right)$ in the given differential equation.
Hence, the order of the dfifferential equation is $5.$

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