Final answer:
To find the general solution of the given differential equation, we rearrange the equation to separate the variables and integrate both sides. The solution is y = Ce^(-cos(x)).
Step-by-step explanation:
To find the general solution of the given differential equation, we can first rearrange the equation to separate the variables:
x(dy/dx) - y = x²sin(x)
Now, we can rewrite the equation as:
dy/y = (xsin(x))/x dx
Integrating both sides of the equation, we get:
ln|y| = ∫sin(x) dx
Using the integration rules for the sine function, we can further simplify the equation:
ln|y| = -cos(x) + C
Finally, we can exponentiate both sides of the equation to get the general solution:
y = Ce^(-cos(x))