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Linear Algebra With Applications
Found in: Page 425
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Solve the nonlinear differential equations in Exercises 6through 11 using the method of separation of variables:Write the differential equation dxdt=fxasdxfx=dt and integrate both sides.


The solution is x(t)=2t+1

See the step by step solution

Step by Step Solution

Step 1: Simplification for the differential equation

Consider the equation as follows:


Now, separate the variables as follows:


Integrating on both sides as follows:


Substituting the initial condition as follows:

x22=t+C(1)22=0+C          {Qx(0)=1}12=C

Step 2 : Calculation of the solution

Now, substitute the value 12 for C in x22=t+C as follows:


Simplify further as follows:


Hence, the solution for the differential equationdxdt=1x is x(t)=2t+1

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