Final answer:
To solve the differential equation dy/dx = x/4y, integrate both sides and raise the exponential solution to the power of e. The implicit solution is in the form |y| = ke^(x^2/8), where k is a constant.
Step-by-step explanation:
To solve the differential equation dy/dx = x/4y, we can rearrange it to dy/y = x/4dx. Integrating both sides, we get ln|y| = (x^2)/8 + C, where C is the constant of integration. To express the implicit solution in the required form, we can exponentiate both sides to get rid of the natural logarithm, resulting in |y| = e^((x^2)/8 + C). Since e^C is another constant, we can rewrite the solution as |y| = ke^(x^2/8), where k is a constant.