A) \[\frac{67}{12}\]
B) \[5\sin \frac{7}{12}\]
C) \[5\log \frac{7}{12}\]
D) None of these
Correct Answer: C
Solution :
[c] The differential equation is \[\frac{dy}{dx}-\frac{y}{x}=-\frac{5x}{(x+2)(x-3)}\] I.F = \[{{e}^{\int{\left( \frac{1}{x} \right)dx\,}}}\,={{e}^{-ln\,x}}=\frac{1}{x}\] Solution is \[y\left( \frac{1}{x} \right)=\int{\left( \frac{1}{x} \right)\times \frac{5x}{(x+2)(x-3)}dx=ln\left( \frac{x+2}{x-3} \right)+C}\] It passes through (4, 0), so \[C=-ln\,\,6\] \[\therefore \,\,\,y=xln\left\{ \frac{(x+2)}{6(x-3)} \right\}\] Putting (5, a), we get a = 5 \[\ln \,\left( \frac{7}{12} \right)\]You need to login to perform this action.
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