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Solve the differential equation $\left(2xy+e^y\right)y^{\prime}+y^2+\cos\left(x\right)=0$

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Solution

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Final answer to the problem

$y^2x+e^y=C_0-\sin\left(x\right)$
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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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1

Rewrite the differential equation using Leibniz notation

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

$\left(2xy+e^y\right)\frac{dy}{dx}+y^2+\cos\left(x\right)=0$

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Learn how to solve differential equations problems step by step online. Solve the differential equation (2xy+e^y)y^'+y^2cos(x)=0. Rewrite the differential equation using Leibniz notation. Rewrite the differential equation. Group terms with common factors. Rewrite the differential equation.

Final answer to the problem

$y^2x+e^y=C_0-\sin\left(x\right)$

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Plotting: $y^2x+e^y=C_0-\sin\left(x\right)$

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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

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

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

$\frac{dy}{dx}=\frac{\sin\left(x\right)}{e^y}$

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

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

$xdx+ydy=0$

Main Topic: Differential Equations

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

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