Students can Download Maths Chapter 9 Differential Equations Ex 9.1 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka 2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.1

### 2nd PUC Maths Differential Equations NCERT Text Book Questions and Answers Ex 9.1

Determine order and degree (if defined) of differential equations given in

Exercises 1 to 10.

Question 1.

\(\frac { d^{ 4 }y }{ dx^{ 4 } } +\sin \left( y^{ \prime \prime \prime } \right) =0\)

Answer:

higher order is \(\frac{\mathrm{d}^{4} \mathrm{y}}{\mathrm{d} \mathrm{x}^{4}}\) so order is 4

As it is not a polynomial in \(\frac{d y}{d x}\) degree is not defined.

Question 2.

y’+5y = 0

Answer:

\(\left(\frac{d y}{d x}\right)+5 y=0\)

here order is 1 and hence degree is 1.

Question 3.

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

Answer:

\(\left(\frac{\mathrm{ds}}{\mathrm{dt}}\right)^{4}+3 \mathrm{s}\left(\frac{\mathrm{d}^{2} \mathrm{s}}{\mathrm{dt}^{2}}\right)^{1}=0\)

here order is 2 and hence degree is 1.

Question 4.

\(\left(\frac{\mathbf{d}^{2} \mathbf{y}}{\mathbf{d x}^{2}}\right)^{2}+\cos \left(\frac{\mathbf{d} \mathbf{y}}{\mathbf{d x}}\right)=\mathbf{0}\)

Answer:

here order is 2 .As it is not a polynomial in \(\frac{\mathrm{d} y}{\mathrm{d} x}\),degree is not defined.

Question 5.

\(\frac{d^{2} y}{d x^{2}}=\cos 3 x+\sin 3 x\)

Answer:

\(\left(\frac{d^{2} y}{d x^{2}}\right)^{1}=\cos 3 x+\sin 3 x\)

here order is 2 and hence degree is 1.

Question 6.

(y”’)^{2} + (y”)^{3} + (y’)^{4} + y^{5} = 0

Answer:

here the order is 3 and hence degree is 2.

Question 7.

y”’ + 2y’+y’ = 0

Answer:

(y”) + 2y’ + y’ = 0

here the order is 3 and hence the degree is 1.

Question 8.

y’ + y = e^{x
}Answer:

(y’) + y = e^{x
}here the order is 1 and hence the degree is 1.

Question 9.

y’ + (y’)^{2}+2y = 0

Answer:

(y”)’ + (y’)^{2} +2y = 0

here the order is 2 and hence degree is 1.

Question 10.

y’+2y’ + sin y = 0

Answer:

(y”)’ + 2y’ + sin y = 0

degree is 2 and hence degree is 1.

Question 11.

\(\left(\frac{\mathbf{d}^{2} \mathbf{y}}{\mathbf{d x}^{2}}\right)^{3}+\left(\frac{\mathbf{d y}}{\mathbf{d x}}\right)^{2}+\sin \left(\frac{\mathbf{d y}}{\mathbf{d x}}\right)+\mathbf{1}=\mathbf{0}\)

degree is ………….

(A) 3

(B) 2

(C) 1

(D) not defined

Answer:

Since the equation is not a polynomial in

\(\frac{d y}{d x}\) degree is not defined,

hence the answer is (D)

Question 12.

The order of the differential equation

\(2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0\)

(A) 2

(B) 1

(C) 0

(D) not defined

Answer:

Here the highest order is 2.

hence the order is 2.

hence the correct answer is (A)