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प्रश्न
After using \[y=vx\] and writing the right-hand side as \[g(v)\], which separable form is obtained?
पर्याय
\[\frac{dv}{g(v)+v}=\frac{dx}{x}\]
\[\frac{dx}{g(v)-v}=\frac{dv}{v}\]
\[\frac{dv}{g(v)-v}=\frac{dx}{x}\]
\[\frac{dv}{g(v)-v}=\frac{dy}{y}\]
MCQ
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उत्तर
Substitution gives \[v+x\frac{dv}{dx}=g(v)\]. Thus \[x\frac{dv}{dx}=g(v)-v\], which separates as \[\frac{dv}{g(v)-v}=\frac{dx}{x}\].
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