Explanation Given: The given differential equation is, ( 2 x + y + 1 ′ ) y ′ = 1 Calculation: Consider the given differential equation. ( 2 x + y + 1 ′ ) y ′ = 1 Substitute d y d x for y ′ and rewrite the above differential equation. ( 2 x + y + 1 ) d y d x = 1 d y d x = 1 2 x + y + 1 (1) Substitute u for 2 x + y + 1 and differentiate u with respect to x . d u d x = 2 + d y d x d y d x = d u d x − 2 Substitute d u d x − 2 for d y d x and u for 2 x + y + 1 in equation (1). d u d x − 2 = 1 u d u d x = 1 u + 2 d u d x = 1 + 2 u u u 1 + 2 u d u = d x Further solve the above equation. 1 2 ( 2 u 1 + 2 u ) d u = d x 1 2 ( 1 + 2 u − 1 1 + 2 u ) d u = d x 1 2 ( 1 + 2 u 1 + 2 u − 1 1 + 2 u ) d u = d x 1 2 ( 1 − 1 1 + 2 u ) d u = d x Integrate the above equation

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ISBN: 9781337810906

Author: ZILL

Publisher: CENGAGE L

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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The solution of the given differential equation.

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Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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The solution of the given differential equation.

Solution Summary: The author explains the solution of the given differential equation: 2y-2-mathrmlnleft|4x+2y+3right|=C.

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