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

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{x^{3}}{3}+x^2+x+C_0$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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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

$dy=\left(x+1\right)^2dx$

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

$dy=\left(x+1\right)^2dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(x+1)^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 \left(x+1\right)^2dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(x^{2}+2x+1\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$y=\frac{x^{3}}{3}+x^2+x+C_0$

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Function Plot

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

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5
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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

How to improve your answer:

Similar Problems Solved

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

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

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

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

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

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

$\frac{dy}{dx}=y\left(1-y\right)$

Main Topic: Differential Equations

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

Used Formulas

See formulas (4)

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