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. ( y - cos2 x ) dx + cos x dy = 0
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. ( y - cos2 x ) dx + cos x dy = 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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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. ( y - cos2 x ) dx + cos x dy = 0
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