The differential equation x ( d^2 y d x^2 )^3 + ( dy dx )^4 + y =… - Vidyadip

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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