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Solve the differential equation $\frac{dy}{dx}=\frac{2000-17.5y}{3500}$

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Solution

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Final answer to the problem

$-200\ln\left|-7y+800\right|=x+C_0$
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Step-by-step Solution

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1

Group the terms of the differential equation. Move the terms of the $y$ variable to the left side, and the terms of the $x$ variable to the right side of the equality

Learn how to solve trigonometric integrals problems step by step online.

$\frac{3500}{2000-17.5y}dy=dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the differential equation dy/dx=(2000-17.5y)/3500. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{3500}{2000-17.5y}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Simplify the division 3500 by 2.5.

Final answer to the problem

$-200\ln\left|-7y+800\right|=x+C_0$

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Function Plot

Plotting: $\frac{dy}{dx}+\frac{-2000+17.5y}{3500}$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

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