Find the solution of the following Differential Equations. \frac{xdy-ydx}{x^{2}}=0

eiraszero11cu

eiraszero11cu

Answered question

2021-12-26

Find the solution of the following Differential Equations.
xdyydxx2=0

Answer & Explanation

Vivian Soares

Vivian Soares

Beginner2021-12-27Added 36 answers

xdyydxx2=0
xx2dyyx2dx=0
yx2dx+1xdy=0
Mdx+Ndy=0
M=yx2,N=1x
Then my=1x2 and Nx=1x2
Clearly my=Nx=1x2
The given differential equation is exact
Hence, the general solution is
Mdx+Ndy=c, where c is constant
yx2dx+0=c
y(1x)=c
yx=c or y=cx
Answer: y=cx where c is an arbitrary constant.
Hector Roberts

Hector Roberts

Beginner2021-12-28Added 31 answers

xdyydxx2=0
(1x)dy(yx2)dx=0
d(yx)=0
yx=C, C constants
y=Cx.
karton

karton

Expert2022-01-09Added 613 answers

(xdyydx)/(x2)=0(xdyydx)=0xdy=ydx(1/y)dy=(1/x)dx(1/x)dx(1/y)dy=0lnxlny=constantln(x)ln(y)=ln(c)ln(x/y)=ln(c)x/y=cx=cyy=(1/c)xy=Cx[here C=1/c]

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