Classify the following differential equations as separable, homogeneous, parallel line,

Inyalan0 2021-12-30 Answered
Classify the following differential equations as separable, homogeneous, parallel line, or exact. Explain briefly your answers. Then, solve each equation according to their classification. 2xsin2ydx(x29)cosydy=0
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Philip Williams
Answered 2021-12-31 Author has 39 answers
Given differential equation
2xsin2ydx(x29)cosydy=0
write the equation in the standard form
dydx=2xsin2y(x29)cosy
we can saperate the variable so, equation is seperable now seperating the variable
(cosysin2y)dy=(2xx29)dx
integrate both side
(cosysin2y)dy=(2xx29)dx
d(siny)sin2y=d(x29)x29
1siny=ln(x29)+C
ln(x29)+cos ec y=C
hence solution of differential equation is
ln(x29)+cos ec y=C
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temnimam2
Answered 2022-01-01 Author has 36 answers
2xsin2ydx(x29)cosydy=0
2xsin2ydx=(x29)cosydy
2x(x29)dx=cosysin2ydy
2x(x29)dx=cosec ycotydy
This is variable separable form.
the general solution is
2xx29dx=cosecycotydy
ln|x29|=cosec y+c
This is general solution.
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karton
Answered 2022-01-09 Author has 439 answers

dydx=2xsin2y(x29)cosy(cosysin2y)dy=(2xx29)dx(cosysin2y)dy=(2xx29)dxd(siny)sin2y=d(x29)x291siny=ln(x29)+Cln(x29)+cos ec y=CAnswer:ln(x29)+cosec y=C

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In studying a reflection-transmission problem involving exotic materials, I have come across the following linear first-order differential equation:A∂∂tg(t)+Bg(t)=f(t),(1)where A and B are constants, g(t) is associated with the reflected wave, and f(t) is a (finite) driving function associated with the incident wave. Both A and B may be positive or negative. I am interested in the behavior of the solution in the limit that A\rightarrow0.
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