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True or False:
The general solution for the equation tx˙=x is x=ct.

2 Answers

5 votes

Final answer:

The general solution for the equation tx˙=x is x= Ce^(ln|t|).

Step-by-step explanation:

The equation tx˙=x can be rearranged to solve for x. Dividing both sides of the equation by t gives us x˙=x/t. Then, integrating both sides of the equation with respect to t gives us ln|x| = ln|t| + C, where C is a constant of integration. Taking the exponent of both sides of the equation gives us x = e^(ln|t| + C). Since e^(ln|t| + C) = e^C * e^(ln|t|), we can rewrite the equation as x = Ce^(ln|t|), where C = e^C. Therefore, the general solution for the equation tx˙=x is x= Ce^(ln|t|).

User Eugene Khyst
by
9.0k points
1 vote

Answer:

True

Step-by-step explanation:

The general solution for the equation tx˙=x is x=ct.

User David Csonka
by
8.6k points

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