Find the general solution to the differential equation .

Question

Find the general solution to the differential equation  . ​

Quizplus · Accepted Answer

The given differential equation is a separable one, which means that we can write it in the form:

$$ \frac{dy}{dx} = \frac{11y}{x} $$

Separating the variables and integrating both sides, we get:

$$ \int \frac{1}{y} dy = \int \frac{11}{x} dx $$

which simplifies to:

$$ \ln|y| = 11\ln|x| + C $$

(where C is an arbitrary constant of integration).

Taking exponential of both sides, we get:

$$ |y| = e^{11\ln|x| + C} = e^C |x|^{11} $$

or:

$$ y = \pm e^C x^{11} $$

(where the $\pm$ sign indicates that there are two families of solutions depending on whether y is positive or negative).

Thus, the general solution to the given differential equation is given by:

$$ y = Ae^{|x|^{11}}, A 
eq 0 $$

where A is an arbitrary non-zero constant.

Find the General Solution to the Differential Equation