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Linear Algebra With Applications
Found in: Page 442
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 differential equation dxdt+3x=7 and find the solution of the differential equation.

The solution is f(t)=73+73e-3tC .

See the step by step solution

Step by Step Solution

Step1: Definition of first order linear differential equation

Consider the differential equation f'(t)-af(t)=g(t) where g(t) is a smooth function and 'a' is a constant. Then the general solution will be f(t)=eate-atg(t)dt.

Step2: Determination of the solution

Consider the differential equation as follows.


Now, the differential equation is in the form as follows.

f'(t)-af(t)=g(t), where g(t) is a smooth function, then the general solution will be as follows.


Step3: Compute the calculation of the solution

Substitute the value7 for g(t) and -3 for in f(t)=eate-atg(t)dt as follows.


Using substitution method in the integral as follows.


Substitute the value 3t fory and dy3 for dt in f(t)=7e3te-3tdt as follows.


Now, undo the substitution as follows.


Hence, the solution for the linear differential equationx'(t)+3x(t)=7 is f(t)=73+73e-3tC

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