12th NCERT Differential Equation Exercise 9.1 Number of questions 12

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Determine order and degree ( if defined) of deifferential equations given in Exercise 1 to 10

Question (1)

\[\frac{{{d^4}y}}{{d{x^4}}} + \sin \left( {y'''} \right) = 0\]

Solution

Order : 4
Degree not define as composite function of derivative

Question (2)

y' + 5y = 0

Solution

Order : 1
Degree : 1

Question (3)

\[{\left( {\frac{{ds}}{{dt}}} \right)^4} + 3s\frac{{{d^2}s}}{{d{t^2}}} = 0\]

Solution

Order : 2
Degree : 1

Question (4)

\[{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^2} + \cos \left( {\frac{{dy}}{{dx}}} \right) = 0\]

Solution

Order : 2
Degree not define as composite

Question (5)

\[\frac{{{d^2}y}}{{d{x^2}}} = \cos 3x + \sin 3x\]

Solution

Order : 2
Degree: 1

Question (6)

(y''')² + (y'')³ + (y')⁴ + y⁵ = 0

Solution

Order : 3
Degree: 2

Question (7)

y''' +2 y'' + y' = 0

Solution

Order : 3
Degree: 1

Question (8)

y' + y = e^x

Solution

Order : 1
Degree: 1

Question (9)

y'' + (y')² + 2y = 0

Solution

Order : 2
Degree: 1

Question (10)

y'' + 2y' + siny = 0

Solution

Order : 2
Degree: 1

Question (11)

The degree of the differential equation
\[{\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^3} + {\left( {\frac{{dy}}{{dx}}} \right)^2} + \sin \left( {\frac{{dy}}{{dx}}} \right) + 1 = 0\] (A) 3   (B) 2   (C) 1   (D) not defined

Solution

Degree4 is not defined
Option (D) is Correct

Question (12)

The order of the differential equation \[2{x^2}\frac{{{d^2}y}}{{d{x^2}}} - 3\frac{{dy}}{{dx}} + y = 0\] (A) 2   (B) 1   (C) 0   (D) not defined

Solution

Order : 2
Option (A) is correct