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jolli1 [7]
3 years ago
12

Solve the differential equation. (dy)/(dx) = 10 sqrt(x)/e^y

Mathematics
2 answers:
Airida [17]3 years ago
7 0
We will do seperation of variables

group y's with dy and x  with dx
integrate both sides, and add constant to one side
use initial condiiton (if applcable)
solve for y



so

dy/dx=10(√x)/(e^y)
times both sides by e^y times dx
e^y dx=10(√x) dx
integrate both sides
an antiderivitive of 10(√x) is 10 times the antiderivitive of x^ \frac{1}{2} which is \frac{x^\frac{3}{2}}{ \frac{3}{2} } or \frac{2x^\frac{3}{2}}{3}
e^y=\frac{20x^\frac{3}{2}}{3} +C
take the ln of both sides
y=ln(\frac{20x^\frac{3}{2}}{3}+C)
nadya68 [22]3 years ago
5 0
See photo for solution


y = ln(20x^(3/2) / 3 + C)

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