Determine whether the following differential equation is exact. If it is exact, solve it. y(xy + 2x^2y^2)dx + x(xy − x^2y^2) dy = 0 b) Solve the given initial value-problem: (x + y)^2 dx + (2xy + x^2 − 1) dy = 0, y(1) = 1. c)Find the general solution of the given higher order differential equation: y^4 + y′′′ + y′′ = 0
Determine whether the following differential equation is exact. If it is exact, solve it. y(xy + 2x^2y^2)dx + x(xy − x^2y^2) dy = 0 b) Solve the given initial value-problem: (x + y)^2 dx + (2xy + x^2 − 1) dy = 0, y(1) = 1. c)Find the general solution of the given higher order differential equation: y^4 + y′′′ + y′′ = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 a) Determine whether the following differential equation is exact. If it is exact,
solve it. y(xy + 2x^2y^2)dx + x(xy − x^2y^2) dy = 0
b) Solve the given initial value-problem:
(x + y)^2 dx + (2xy + x^2 − 1) dy = 0, y(1) = 1.
c)Find the general solution of the given higher order differential equation:
y^4 + y′′′ + y′′ = 0
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