# Solve the following differential equation : $\large \frac{dy}{dx}$$+y=\cos\: x-\sin\: x ## 1 Answer Toolbox: • To solve the first order linear differential equation of the form \large\frac{dy}{dx}$$ + Py = Q$
• (i) Write the given equation in the form of $\large\frac{dy}{dx}$$+ Py = Q • (ii) Find the integrating factor (I.F) = e^{\int Pdx}. • (iii) Write the solution as y(I.F) = integration of Q(I.F) dx + C • \int e^x[f(x)+f'(x)]dx=e^xf(x)+c Step 1: Given :\large\frac{dy}{dx}$$+y=\cos x-\sin x$
This is a linear differential equation of the form