A) \[{{e}^{3x}}+3{{e}^{-4y}}=4\]
B) \[4{{e}^{3x}}-3{{e}^{-4y}}=3\]
C) \[3{{e}^{3x}}+4{{e}^{-4y}}=7\]
D) \[4{{e}^{3x}}+3{{e}^{-4y}}=7\]
Correct Answer: C
Solution :
Give, \[\log \left( \frac{dy}{dx} \right)=3x+4y\] \[\Rightarrow \]\[\frac{dy}{dx}={{e}^{3x}}{{e}^{4y}}\] \[\Rightarrow \]\[{{e}^{-4y}}dy={{e}^{3x}}dx\] On integrating both sides, we get \[-4{{e}^{-4y}}=3{{e}^{3x}}+c\] At \[x=0,y=0,\] \[-4=3+c\Rightarrow c=-7\] \[\therefore \] Solution is \[4{{e}^{-4y}}+3{{e}^{3x}}=7\]You need to login to perform this action.
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