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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The differential equation $x{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^3} + {\left( {\frac{{dy}}{{dx}}} \right)^4} + y = {x^2}$ is of
  • ✓
    Degree $3$ and order $2$
  • B
    Degree $1$ and order $1$
  • C
    Degree $4$ and order $3$
  • D
    Degree $4$ and order $4$
✓

Answer

Correct option: A.
Degree $3$ and order $2$
a
(a) Given differential equation, $x{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^3} + {\left( {\frac{{dy}}{{dx}}} \right)^4} + y = {x^2}$

In this equation order of highest derivative is $2,$

Hence order $ = 2$ and degree of highest derivative $ = 3$.

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