To determine The curve through the origin in the xy -plane which satisfies y ″ = 2 y ′ whose the tangent at the origin has the slope 1. Explanation The given ODE is y ″ = 2 y ′ . Reduce the ODE y ″ = 2 y ′ to first order as follows. Let z = y ′ , that implies, z ′ = y ″ . Substitute z = y ′ and z ′ = y ″ in y ″ = 2 y ′ and simplify further. z ′ = 2 z d z d x = 2 z [ ∵ z ′ = d z d x ] Hence, the first order equation. Separate the variables as follows. d z d x = 2 z d z z = 2 d x Now integrate the above equation as follows. ∫ d z z = 2 ∫ d x ln | z | = 2 x + C e ln | z | = e 2 x + C Z = C 1 e 2 x [ ∵ e C = C

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ISBN: 9781119664697

Author: Kreyszig

Publisher: WILEY

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Chapter 2.1, Problem 11P

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The curve through the origin in the xy-plane which satisfies y″=2y′ whose the tangent at the origin has the slope 1.

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Chapter 2.1, Problem 10P

Chapter 2.1, Problem 12P

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