Solve the following Differential Equation in LINEAR DE of Order One 1. (3xy + 3y - 4) dx + (x + 1)2 dy = 0
Solve the following Differential Equation in LINEAR DE of Order One 1. (3xy + 3y - 4) dx + (x + 1)2 dy = 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
Related questions
Question
Linear DE of Order One
Standard form : dy/dx + P(x) y = Q(x)
where P and Q are both functions of x
when the independent variable is y, the std form is
dx/dy + P(y) x = Q(y)
where P and Q are both functions of y
Solutions Steps:
1. Put the equation into the standard form.
2. Solve for integrating factor θ
θ = e∫P(x)dx or θ = e∫P(y)dy
3. Multiply both sides of equation by θ
4. Integrate both sides of equation to get the General Solution.
(The integral of the left side is always equal to yθ or xθ)
General Solution:
yθ = ∫ Q(x) θ dx + C
or xθ = ∫ Q(y) θ dy + C
Solve the following Differential Equation in LINEAR DE of Order One
1. (3xy + 3y - 4) dx + (x + 1)2 dy = 0
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning