Question

70. The solution of the differential equation x4 dy+x3y=- sec (xy) would be
dx
1
A) sin xy = +
2r
B) sin xy
C) sin xy =
2x
D) sin xy =
2y?
2y
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Answer 1

Step-by-step explanation:

70. The solution of the differential equation x4 dy+x3y=- sec (xy) would be

dx

1

A) sin xy = +

2r

B) sin xy

C) sin xy =

2x

D) sin xy =

2y?

2y

lovi

iiven by

Someone solve this question I don't know to solve maths.

Answer 2

Answer:

The answer is   $2sin(xy)+x^{-2}=c$.

Step-by-step explanation:

Step 1:

The differential equation given is $x^{4} \frac{dy}{dx} +x^{3}y=-sec(xy)$

$\implies x^{4} dy +x^{3}y\hspace{.1cm}dx=-sec(xy)dx$

Step 2:

Taking $x^{3}$  common,

$\implies x^{3} (xdy +y\hspace{.1cm}dx)=-sec(xy)dx$

$\implies x^{3} \hspace{.1cm} d(xy)=-sec(xy)dx$                       .....[  $d(xy)=xdy+ydx$  ]

$\implies \frac{dx}{x^{3} } = \frac{d(xy)}{-sec(xy)}$

Step 3:

Integrating both sides,

∫$\frac{dx}{x^{3} }=$∫$\frac{d(xy)}{-sec(xy)}$

$\implies$ ∫$x^{-3} dx$  $=$   -∫ $cos(xy)$                          ...[ $\frac{1}{sec\theta} =cos\theta$ ]

$\implies \frac{x^{-2} }{-2} =-sin(xy)+c$

$\implies 2sin(xy)+x^{-2}=c$

The answer is   $2sin(xy)+x^{-2}=c$.

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