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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 $True$

 

answered May 22, 2013 by meena.p
 

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