The general solution of y dx-x dy-ny2tanxy dx isWhere C is the constant of integration and n-

(y dx x dy)=ny^2tan(xy) dx nbsp; ⇒(xy)ydx xdyy^2=ndx ⇒(xy)d (xy)=ndx On integration, we get ∫(xy)d (xy)=∫ ndx ⇒ln(sinxy)=nx+ln C ⇒sinxy=e^nx+ln C=Ce^nx ...

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Standard IX

History

Machiavelli

The general s...

Question

The general solution of $(y d x - x d y) = n y^{2} tan (\frac{x}{y}) d x$ is
$($ Where $C$ is the constant of integration and $n \in R)$

sin (\frac{x}{y}) = C e^{n x}

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x = C n y

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cos (\frac{x}{y}) = C e^{n x}

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\frac{x}{y} = C e^{n x}

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Solution

The correct option is A $sin (\frac{x}{y}) = C e^{n x}$
$(y d x - x d y) = n y^{2} tan (\frac{x}{y}) d x$
$\Rightarrow cot (\frac{x}{y}) \frac{y d x - x d y}{y^{2}} = n d x$
$\Rightarrow cot (\frac{x}{y}) d (\frac{x}{y}) = n d x$
On integration, we get
$\int cot (\frac{x}{y}) d (\frac{x}{y}) = \int n d x$
$\Rightarrow ln (sin \frac{x}{y}) = n x + ln C$
$\Rightarrow sin \frac{x}{y} = e^{n x + ln C} = C e^{n x}$

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The general solution of (y dx−x dy)=ny2tan(xy)dx is (Where C is the constant of integration and n∈R)

The correct option is A sin(xy)=Cenx(y dx−x dy)=ny2tan(xy)dx ⇒cot(xy)ydx−xdyy2=ndx ⇒cot(xy)d(xy)=ndx On integration, we get ∫cot(xy)d(xy)=∫ndx ⇒ln(sinxy)=nx+lnC ⇒sinxy=enx+lnC=Cenx

The general solution of $(y d x - x d y) = n y^{2} tan (\frac{x}{y}) d x$ is
$($ Where $C$ is the constant of integration and $n \in R)$