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In exercises 16-20, integrate both sides of each of the following differential equations once from 0 to x, and use the given initial condition to convert to a corresponding integral equation or integro-differential equation. (Follow Example 1.) (16) u'(x) = 4u(x), u(0) = 1. (17) u(x) = 3x²u(x), u(0) = 1. (18) u'(x) = u?(x), u(0) = 4. %3D

In exercises 16-20, integrate both sides of each of the following differential equations once from 0 to x, and use the given initial condition to convert to a corresponding integral equation or integro-differential equation. (Follow Example 1.) (16) u'(x) = 4u(x), u(0) = 1. (17) u(x) = 3x²u(x), u(0) = 1. (18) u'(x) = u?(x), u(0) = 4. %3D

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 16E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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In exercises 16-20, integrate both sides of each of the following differential equations once from 0 to x, and use the given initial condition to convert to a corresponding integral equation or integro-differential equation. (Follow Example 1.) (16) и(х) %3D 4u(х), и(0) %3D1. (17) «(х) %3 Зx-и(х), и(0) — 1. (18) и (х) %3 и?(х), и(0) %3 4. (19) и"(х) %3 4хи?(х), и(0) %3D2, и'(0) %3D1. (20) и"(х) %3D2хи(х), и(0) %3D0, и(0) %3D1.
Transcribed Image Text:In exercises 16-20, integrate both sides of each of the following differential equations once from 0 to x, and use the given initial condition to convert to a corresponding integral equation or integro-differential equation. (Follow Example 1.) (16) и(х) %3D 4u(х), и(0) %3D1. (17) «(х) %3 Зx-и(х), и(0) — 1. (18) и (х) %3 и?(х), и(0) %3 4. (19) и"(х) %3 4хи?(х), и(0) %3D2, и'(0) %3D1. (20) и"(х) %3D2хи(х), и(0) %3D0, и(0) %3D1.
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