The solution of y^5 x + y - x dy dx = 0 is - Vidyadip

MCQ

The solution of ${y^5}x + y - x\frac{{dy}}{{dx}} = 0$ is

A
${x^4}/4 + 1/5{(x/y)^5} = C$
✓
${x^5}/5 + (1/4){(x/y)^4} = C$
C
${(x/y)^5} + {x^4}/4 = C$
D
none of these

✓

Answer

Correct option: B.

${x^5}/5 + (1/4){(x/y)^4} = C$

b
The given differential equation can be written as $\mathrm{y}^{5} \mathrm{xdx}+\mathrm{ydx}-\mathrm{xdy}=0 .$ Multiplying by

$\mathrm{x}^{3} / \mathrm{y}^{5},$ we have

$x^{4} d x+\frac{x^{3}}{y^{3}}\left(\frac{y d x-x d y}{y^{2}}\right)=0$

Integrating, we get $x^{5} / 5+(1 / 4)(x / y)^{4}=C$

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