Question

The general solution of the differential equation of the type $\frac{dx}{dy}+Rx=S,$ Where R and S are function of y, is _________________.

Answer 1

Given: $\frac{dx}{dy}+Rx=S,$ where R and S are function of y


$\frac{dx}{dy}+Rx=S$

The given equation is linear differential equation.

Integrating factor (I.F.) = $e^{\int Rdy}$

The required solution is

$x{e}^{\int Rdy}=\int \left(S{e}^{\int Rdy}\right)dy+C,\mathrm{where}C\mathrm{is}\mathrm{arbitrary}\mathrm{constant}$

Hence, the general solution of the differential equation of the type $\frac{dx}{dy}+Rx=S,$ where R and S are function of y, is $\underline{x{e}^{\int Rdy}=\int \left(S{e}^{\int Rdy}\right)dy+C}$.