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Solve the differential equation $y=y^{\prime}+x$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$y=x+1+C_0e^x$
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Step-by-step Solution

How should I solve this problem?

  • Choose an option
  • 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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1

Rewrite the differential equation using Leibniz notation

Learn how to solve integration by parts problems step by step online.

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

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Unlock the first 3 steps of this solution

Learn how to solve integration by parts problems step by step online. Solve the differential equation y=y^'+x. Rewrite the differential equation using Leibniz notation. Group the terms of the equation. Divide all the terms of the differential equation by -1. Simplifying.

Final answer to the problem

$y=x+1+C_0e^x$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $y=x+1+C_0e^x$

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Got a different answer? Verify it!

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1
2
3
4
5
6
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

$\left(x^2+1\right)\frac{dy}{dx}+3xy=6x$

$dy=\left(x-3y\right)dx$

$\frac{dy}{dx}+4y=8$

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

$\frac{dy}{dx}=e^{x-y}+e^x+e^{-y}+1$

$\frac{dy}{dx}=\left(x-y+5\right)^2$

$\frac{dy}{dx}=x-2y+12$

Main Topic: Integration by Parts

Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.

Used Formulas

See formulas (6)

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