Find the general solution of the given differential equation. x dy/dx -y= x² sin(x)

Solution:

x dx/dy - y = x² sin (x)

First, divide both sides by x²

By doing this any possible solution exists on either (-∞, 0) or (0, ∞)

1/x dy/dx - y/x² = sin x

Now condense the left side as a derivative of a product and integrate both sides and solve for y

d/dx [y/x] = sin x

y/x = ∫ sin x dx

y = Cx - x cos x

Therefore, the general solution is y = Cx - x cos x.

Find the general solution of the given differential equation.
x dy/dx -y= x² sin(x)

Summary:

The general solution of the given differential equation x dy/dx -y= x² sin(x) is y = Cx - x cos x.