The general solution of a differential equati | vedclass

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(A) The given differential equation is of the form $\frac{dx}{dy} + P_{1}x = Q_{1}$,where $P_{1}$ and $Q_{1}$ are functions of $y$ only.The integratin

Vedclass · Accepted Answer

$x \cdot e^{\int P_{1} dy} = \int (Q_{1} \cdot e^{\int P_{1} dy}) dy + C$

Vedclass · Answer

(A) The given differential equation is of the form $\frac{dx}{dy} + P_{1}x = Q_{1}$,where $P_{1}$ and $Q_{1}$ are functions of $y$ only.The integrating factor ($I$.$F$.) for this differential equation is given by:$I.F. = e^{\int P_{1} dy}$The general solution of the differential equation is given by:$x \cdot (I.F.) = \int (Q_{1} \cdot I.F.) dy + C$Substituting the value of the integrating factor:$x \cdot e^{\int P_{1} dy} = \int (Q_{1} \cdot e^{\int P_{1} dy}) dy + C$Comparing this with the given options,the correct option is $A$.

The general solution of a differential equation of the type $\frac{dx}{dy} + P_{1}x = Q_{1}$ is

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