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

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## 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.
$$\frac { d^{ 4 }y }{ dx^{ 4 } } +\sin \left( y^{ \prime \prime \prime } \right) =0$$
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
$$\left(\frac{d y}{d x}\right)+5 y=0$$
here order is 1 and hence degree is 1.

Question 3.
$$\left(\frac{d s}{d t}\right)^{4}+3 s \frac{d^{2} s}{d t^{2}}=0$$
$$\left(\frac{\mathrm{ds}}{\mathrm{dt}}\right)^{4}+3 \mathrm{s}\left(\frac{\mathrm{d}^{2} \mathrm{s}}{\mathrm{dt}^{2}}\right)^{1}=0$$
here order is 2 and hence degree is 1.

Question 4.
$$\left(\frac{\mathbf{d}^{2} \mathbf{y}}{\mathbf{d x}^{2}}\right)^{2}+\cos \left(\frac{\mathbf{d} \mathbf{y}}{\mathbf{d x}}\right)=\mathbf{0}$$
here order is 2 .As it is not a polynomial in $$\frac{\mathrm{d} y}{\mathrm{d} x}$$,degree is not defined.

Question 5.
$$\frac{d^{2} y}{d x^{2}}=\cos 3 x+\sin 3 x$$
$$\left(\frac{d^{2} y}{d x^{2}}\right)^{1}=\cos 3 x+\sin 3 x$$
here order is 2 and hence degree is 1.

Question 6.
(y”’)2 + (y”)3 + (y’)4 + y5 = 0
here the order is 3 and hence degree is 2.

Question 7.
y”’ + 2y’+y’ = 0
(y”) + 2y’ + y’ = 0
here the order is 3 and hence the degree is 1.

Question 8.
y’ + y = ex
(y’) + y = ex
here the order is 1 and hence the degree is 1.

Question 9.
y’ + (y’)2+2y = 0
(y”)’ + (y’)2 +2y = 0
here the order is 2 and hence degree is 1.

Question 10.
y’+2y’ + sin y = 0
(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
Since the equation is not a polynomial in
$$\frac{d y}{d x}$$ degree is not defined,

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