# True-or-False: Solution of the differential equation of the type $\large\frac{dx}{dy}$$+P_1x=Q_1 is given by x.(I.F)=\int (I.F)Q_1dy. ## 1 Answer Toolbox: • A homogeneous linear differential equation of the form \large\frac{dy}{dx}$$+Py=Q$ has an integral factor $e^{\int pdx}$
• The solution is $xe^{\int pdy} =\int Q.e^{\int pdy}dy+c$
Whenever a linear differential equation is of the form $\large\frac{dx}{dy}$$+Py=Q Where p and Q are functions of y or constants. Here y is the independent variable. and x is the depentdent variable. Hence the integrating factor is e^{\int pdy} The solution is xe^{\int pdy} =\int Q.e^{\int pdy}dy+c Therefore Solution of the differential equation of the type \large\frac{dx}{dy}$$+P_1x=Q_1$ is given by $x.(I.F)=\int (I.F)Q_1dy.$ is $True$