2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5

   

Students can Download Maths Chapter 9 Differential Equations Ex 9.5 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 9.5

2nd PUC Maths Differential Equations NCERT Text Book Questions and Answers Ex 9.5

In each of the Exercises 1 to 10, show that the given differential equation is homogeneous and solve each of them.

Question 1.
(x2 + xy) dy = (x2 + y2) dx
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.1
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.2

Question 2.
\(y^{\prime}=\frac{x+y}{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.3
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.4

Question 3.
(x- y)dy – dy -(x+y)dx = o
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.5

2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.6

KSEEB Solutions

Question 4.
(x2 – y2) dx + 2xy dy =0
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.7

Question 5.
\(x^{2} \frac{d y}{d x}=x^{2}-2 y^{2}+x y\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.8
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.9

Question 6.
\(\mathbf{x} \mathrm{d} \mathbf{y}-\mathbf{y} \mathbf{d x}=\sqrt{\mathbf{x}^{2}+\mathbf{y}^{2}} \mathbf{d} \mathbf{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.10

KSEEB Solutions

Question 7.
\(\left\{x \cos \left(\frac{y}{x}\right)+y \sin \left(\frac{y}{x}\right)\right\} y d x\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.11
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.12
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.13

Question 8.
\(x \frac{d y}{d x}-y+x \sin \left(\frac{y}{x}\right)=0\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.14

KSEEB Solutions

Question 9.
\(y d x+x \log \left(\frac{y}{x}\right) d y-2 x d y=0\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.15
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.16

Question 10.
\(\left(1+e^{\frac{x}{y}}\right) d x+e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) d y=0\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.17
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.18

KSEEB Solutions

For each of the differential equations in Exercises from 11 to 15, find the particular solution satisfying the given condition:

Question 11.
(x + y) dy + (x – y) dx = 0; y = 1 when x = 1
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.19
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.20
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.21

Question 12.
x2dy + (xy + y2) dx = 0; y = 1 when x = 1
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.22
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.23

KSEEB Solutions

Question 13.
\(\left[x \sin ^{2}\left(\frac{y}{x}\right)-y\right] d x+x d y=0 ; y=\frac{\pi}{4}\) when x = 1
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.24

Question 14.
\(\frac{d y}{d x}-\frac{y}{x}+\csc \left(\frac{y}{x}\right)=0 ; y=0 \text { when } x=1\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.25
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.26

Question 15.
\(2 x y+y^{2}-2 x^{2} \frac{d y}{d x}=0 ; y=2 \text { when } x=1\)
Answer:
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.27

KSEEB Solutions

Question 16.
A homogeneous differential equation of the from can be solved by making the subtitution.
(A) y = vx
(B) v = yx
(C) x = vy
(D) x = v
Answer:
Answer(C) x = vy

Question 17.
Which of the following is a homogeneous differential equation ?
(A) (4x + 6y + 5) dy – (3y + 2x + 4) dx = 0
(B) (xy) dx – (x3 + y3) dy = 0
(C) (x3 + 2y2) dx + 2xy dy = 0
(D) y2 dx + (x2 – xy – y2) dy = 0
Answer:
Only y2dx + (x2 – xy + y2) dy = 0 can be expressed in the form
\(\frac{x}{y} \text { or } \frac{y}{x}\)
2nd PUC Maths Question Bank Chapter 9 Differential Equations Ex 9.5.28

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