Verify that $ y(t) = ce^{at} $ solves the differential equation for unlimited growth, $ y' = ay $, with initial condition $ y(0) = c $.If $ y(t) = ce^{at} $, then $ y'(t) = \left( \boxed{} \right) e^{at} = ay $.Therefore, $ y(0) = ce^{a \cdot \boxed{}} = ce^{\boxed{}} = c $.

Given Differential Equation : y1 = ay , y(0) = C i.e. dydt =ayie dyy = adt Integratinh both side we…

Answered: Verify that y(t) = ceat solves the…

Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial condition y(0) = c. If y(t) = cet, then y'(t) = eat = ay. Therefore, y(0) )- cel 1).c.

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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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 differential equations.

Question

Verify that $ y(t) = ce^{at} $ solves the differential equation for unlimited growth, $ y' = ay $, with initial condition $ y(0) = c $.

If $ y(t) = ce^{at} $, then $ y'(t) = \left( \boxed{} \right) e^{at} = ay $.

Therefore, $ y(0) = ce^{a \cdot \boxed{}} = ce^{\boxed{}} = c $.

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