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|).