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# Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1 \begin{array}{1 1}(A)\;x-y-1 = Ce^{-y} \\ (B)\;x+y+1 = Ce^{-2y} \\ (C)\;x+y-1 = Ce^{-y} \\(D)\;x+y+1 = Ce^{-y} \end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • The first order linear equation of the form \large\frac{dx}{dy}$$ + Px = Q$ can be solved as follows:
• (i) Write the given equation in the form of $\large\frac{dx}{dy}$$+ Px = Q • (ii) Find the integrating factor (I.F) = e^{\int Pdy}. • (iii) Write the solution as y(I.F) = \int Q(I.F) dy + C Step 1: Using the given information in the tool box let us rewrite the given equation. Divide throughout by (x+y) \large\frac{dy}{dx} = \frac{1}{(x+y)} Recirprocate on both sides we get, \large\frac{dx}{dy}$$ = x+y$