Q1. Find the general solution of the following differential equations and then find the particular solution which satisfies the stated extra condition. Differential Equation (a) dx x+2 (b) (x² + xy) dx=y² dy (c) - y = e* sin(2x) dx Extra Condition y = 0 when x = -1 y = 1 when x = 2 y = 1 when x = 0 Technique Variable Separation -5 +6y= 10 sin x Substitution Integrating Factor Q2. The motion of a body performing damped forced vibrations is described by the following second order inhomogeneous differential equation d²y dy dx² dx Find the general solution of this equation. (Ensure that your solution includes both the Complementary Function (CF) and the Particular Integral (PI))
Q1. Find the general solution of the following differential equations and then find the particular solution which satisfies the stated extra condition. Differential Equation (a) dx x+2 (b) (x² + xy) dx=y² dy (c) - y = e* sin(2x) dx Extra Condition y = 0 when x = -1 y = 1 when x = 2 y = 1 when x = 0 Technique Variable Separation -5 +6y= 10 sin x Substitution Integrating Factor Q2. The motion of a body performing damped forced vibrations is described by the following second order inhomogeneous differential equation d²y dy dx² dx Find the general solution of this equation. (Ensure that your solution includes both the Complementary Function (CF) and the Particular Integral (PI))
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please solve 1)c)
![Q1. Find the general solution of the following differential equations and then find the
particular solution which satisfies the stated extra condition.
Differential Equation
dy e-y
dx x+2
(a)
=
(b) (x² + xy) = y²
dy
(c) - y = e* sin(2x)
dx
Extra Condition
y = 0 when x = -1
y = 1 when x = 2
y = 1 when x = 0
Technique
Variable Separation
Substitution
Integrating Factor
Q2. The motion of a body performing damped forced vibrations is described by the
following second order inhomogeneous differential equation
d²y 5 +6y= 10 sin x
dx²
dx
Find the general solution of this equation.
(Ensure that your solution includes both the Complementary Function (CF)
and the Particular Integral (PI))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F370a60b6-c15d-4be4-b0e6-8cab3f89106f%2F5b3e06da-8a24-4d7e-b604-d1a90f163d70%2Fwidosxp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1. Find the general solution of the following differential equations and then find the
particular solution which satisfies the stated extra condition.
Differential Equation
dy e-y
dx x+2
(a)
=
(b) (x² + xy) = y²
dy
(c) - y = e* sin(2x)
dx
Extra Condition
y = 0 when x = -1
y = 1 when x = 2
y = 1 when x = 0
Technique
Variable Separation
Substitution
Integrating Factor
Q2. The motion of a body performing damped forced vibrations is described by the
following second order inhomogeneous differential equation
d²y 5 +6y= 10 sin x
dx²
dx
Find the general solution of this equation.
(Ensure that your solution includes both the Complementary Function (CF)
and the Particular Integral (PI))
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