You can Download Samacheer Kalvi 12th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.
Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.6
Solve the following differential equations:
Question 1.
Solution:
This is a Homogeneous differential equation
Seperating the variables
Question 2.
(x3 + y3) dy – x2y dx = 0
Solution:
(x3 + y3) dy – x2y dx = 0
(x3 + y3) dy = x3y dx
This is a Homogeneous differential equation.
Separating the variables
Question 3.
Solution:
This is a Homogeneous differential equation
Seperating the variables
Question 4.
2xydx + (x2 + 2y2) dy = 0
Solution:
2xy dx + (x2 + 2y2) dy = 0
(x2 + 2y2) dy = – 2xy dx
This is a Homogeneous differential equation
Separating the variables
Question 5.
(y2 – 2xy)dx = (x2 – 2xy)dy
Solution:
(y2 – 2xy) dx = (x2 – 2xy) dy
This is a Homogeneous differential equation
Seperating the variables
Question 6.
Solution:
Seperating the variables
Question 7.
Solution:
This is a Homogeneous differential equation
Separating the variables
Question 8.
(x2 + y2) dy = xy dx. It is given that y(1) = 1 and y(x0) = e. Find the value of x0.
Solution:
This is a Homogeneous differential equation
Seperating the variables
Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.6 Additional problems
Question 1.
Solve: (2\(\sqrt{x y}\))dy + y dx = 0
Solution:
Question 2.
Solve: (x3 + 3xy2)dx + (y3 + 3x2y)dy = 0
Solution:
Integrating, we have
Question 3.
Solution:
Which is in terms of v alone.
⇒ the given problem comes under homogeneous type.
Question 4.
Solve: (x2 + y2)dy = xy dx
Solution:
Which is a function in v alone.
⇒ the given problem comes under homogeneous type.
Question 5.
Find the equation of the curve passing through (1, 0) and which has slope \(1+\frac{y}{x}\) at (x, y).
Solution:
Given the curve passes through (1, 0) ⇒ at x = 1, y = 0
0 = log 1 +c ⇒ c = 0