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Solve the differential equation $y\left(x^2-1\right)\frac{dy}{dx}=\frac{2x}{4+x}$

Step-by-step Solution

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Solution

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Final Answer

$y=\sqrt{2\left(\frac{1}{3}\ln\left(x+1\right)-\frac{8}{15}\ln\left(x+4\right)+\frac{1}{5}\ln\left(x-1\right)+C_0\right)},\:y=-\sqrt{2\left(\frac{1}{3}\ln\left(x+1\right)-\frac{8}{15}\ln\left(x+4\right)+\frac{1}{5}\ln\left(x-1\right)+C_0\right)}$
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Step-by-step Solution

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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

$y\cdot dy=\frac{1}{x^2-1}\frac{2x}{4+x}dx$

Learn how to solve differential equations problems step by step online.

$y\cdot dy=\frac{1}{x^2-1}\frac{2x}{4+x}dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation y(x^2-1)dy/dx=(2x)/(4+x). 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{1}{x^2-1}\frac{2x}{4+x}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Take out the constant 2 from the integral.

Final Answer

$y=\sqrt{2\left(\frac{1}{3}\ln\left(x+1\right)-\frac{8}{15}\ln\left(x+4\right)+\frac{1}{5}\ln\left(x-1\right)+C_0\right)},\:y=-\sqrt{2\left(\frac{1}{3}\ln\left(x+1\right)-\frac{8}{15}\ln\left(x+4\right)+\frac{1}{5}\ln\left(x-1\right)+C_0\right)}$

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Function Plot

Plotting: $y\left(x^2-1\right)\frac{dy}{dx}+\frac{-2x}{4+x}$

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0
a
b
c
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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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Similar Problems Solved

$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

$\frac{dy}{dx}=\frac{2x}{3y^2}$

$\frac{dx}{dy}=y+xy$

$dx+e^{3x}dy=0$

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

$\frac{dy}{dx}=e^{3x+2y}$

$y'=x+8$

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

4. See formulas

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