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Solve the differential equation $\frac{dy}{dx}=y+y^2$

Step-by-step Solution

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Solution

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Final answer to the problem

$\ln\left|y\right|-\ln\left|y+1\right|=x+C_0$
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Step-by-step Solution

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Learn how to solve integrals by partial fraction expansion problems step by step online. Solve the differential equation dy/dx=y+y^2. 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}{y+y^2}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{y\left(1+y\right)}dy and replace the result in the differential equation.

Final answer to the problem

$\ln\left|y\right|-\ln\left|y+1\right|=x+C_0$

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Function Plot

Plotting: $\frac{dy}{dx}-y-y^2$

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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

How to improve your answer:

Similar Problems Solved

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

$\frac{dy}{dx}-2y=y^2$

$\frac{dy}{dx}=y^2-9$

$\frac{dy}{dx}=y^2-4$

$\frac{dy}{dx}=y-y^2$

$\frac{dy}{dx}=y\left(y+2\right)$

$\frac{dy}{dx}=\frac{x}{2x-y}$

Main Topic: Integrals by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

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