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The general solution of a differential equation of the type $\large\frac{dx}{dy}$$+p_1x=Q_1\;is$

\[ \begin{array}{l} (A)\quad y\;\mathrm{e}^{\int p_1\mathrm{d}y}=\int\bigg(Q_1\mathrm{e}^{\int p_1\mathrm{d}y}\bigg)dy+C \\ (B)\quad y\;.\mathrm{e}^{\int p_1\mathrm{d}x}=\int \bigg(Q_1\mathrm{e}^{\int p_1\mathrm{d}x}\bigg)dx+C \\ (C)\quad x\;\mathrm{e}^{\int p_1\mathrm{d}y}=\int \bigg(Q_1\mathrm{e}^{\int p_1dy}\bigg)dy+C \\ (D)\quad x\;\mathrm{e}^{\int p_1dx}=\int\bigg(Q_1\mathrm{e}^{\int p_1\mathrm{d}x}\bigg)dx+C \end{array} \]

1 Answer

Toolbox:
  • If the first order linear equation is of the type $\large\frac{dx}{dy}$$+px=Q$,then the solution is x( I.F) = integration Q.(I.F) + C where I.F =$ e^{\int p dy}$
Using the information in the tool box we find that the given equation is of the form $\large\frac{dx}{dy} $$+ Px = Q$
Hence the solution is x(I.F) = integration of Q.(I.F) dx + C
Here the integral factor is $\int pdy$
Hence C is the correct answer.
answered Jul 29, 2013 by sreemathi.v
 

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