Solve the following linear first order differential equations x dy/dx - y = x^2 sinx Solution dy/dx - y/x = x sinx We can find the integrating factor: P(x) = -1/x I = eint(-1/x) I = eLnx^-1 I = 1/x (1/x * y)\' = 1/x * x sinx Integrate both sides y/x = -cosx +c y = -x cos x + cx.