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Solve the differential equation $\frac{dx}{dy}=\frac{xy+y+3x+3}{xy+2y-x-2}$

Step-by-step Solution

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Solution

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Final Answer

$x+1-\ln\left(x+1\right)+2\ln\left(x+1\right)=y-1+\ln\left(y-1\right)+3\ln\left(y-1\right)+C_0$
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Step-by-step Solution

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Factoring by $x$

$\frac{dx}{dy}=\frac{x\left(y+3\right)+y+3}{xy+2y-x-2}$

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$\frac{dx}{dy}=\frac{x\left(y+3\right)+y+3}{xy+2y-x-2}$

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Learn how to solve differential calculus problems step by step online. Solve the differential equation dx/dy=(xy+y3x+3)/(xy+2y-x+-2). Factoring by x. Factoring by y+3. Factoring by x. Factor x\left(y-1\right)+2y-2 by the greatest common divisor 2.

Final Answer

$x+1-\ln\left(x+1\right)+2\ln\left(x+1\right)=y-1+\ln\left(y-1\right)+3\ln\left(y-1\right)+C_0$

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Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $\frac{dx}{dy}+\frac{-xy-y-3x-3}{xy+2y-x-2}$

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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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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