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Home » Mark (√) against the correct answer in the following: The general solution of the DE is A. B. C. D. None of these
Mark (√) against the correct answer in the following: The general solution of the DE \log \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=(\mathrm{ax}+\mathrm{by}) is
A. \frac{-\mathrm{e}^{-b y}}{\mathrm{~b}}=\frac{\mathrm{e}^{\mathrm{ax}}}{\mathrm{a}}+\mathrm{C}
B. \mathrm{e}^{a x}-\mathrm{e}^{-b y}=\mathrm{C}
C. b \mathrm{e}^{a x}+a e^{b y}=C
D. None of these
CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal
Mark (√) against the correct answer in the following: The general solution of the DE \log \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=(\mathrm{ax}+\mathrm{by}) is
A. \frac{-\mathrm{e}^{-b y}}{\mathrm{~b}}=\frac{\mathrm{e}^{\mathrm{ax}}}{\mathrm{a}}+\mathrm{C}
B. \mathrm{e}^{a x}-\mathrm{e}^{-b y}=\mathrm{C}
C. b \mathrm{e}^{a x}+a e^{b y}=C
D. None of these

Solution:

\log \left(\frac{d y}{d x}\right)=(a x+b y)
\begin{array}{l} \frac{d y}{d x}=e^{a x+b y} \\ \frac{d y}{e^{b y}}=e^{a x} d x \end{array}
On integrating on both sides we get \frac{-e^{-b y}}{b}=\frac{e^{a x}}{a}+c (solution of given equation)

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