Chapter 1 - First-Order Differential Equations - 1.6 First-Order Linear Differential Equations - True-False Review - Page 59: c

True

$y'+p(x)y=q(x)$ ___(1) This is linear differential equation Integrating factor:- $\;\;I(x)=e^{\int p(x)dx}$ Multiply (1) by $I(x)$ $e^{\int p(x)dx}y'+p(x)e^{\int p(x)dx}y=q(x)e^{\int p(x)dx}$ $(ye^{\int p(x)dx})^{'}=q(x)e^{\int p(x)dx}$ $(y\cdot I(x))^{'}=q(x)I(x)$ That's why by multiplying the differential equation (1) by integrating factor $I(x)$ the differential equation (1) becomes $(y\cdot I(x))^{'}=q(x)I(x)$.