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Solve the differential equation $\left(p-w\right)dp+dw=0$

Step-by-step Solution

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Solution

Final answer to the problem

$p=w+\sqrt{-2w+C_1},\:p=w-\sqrt{-2w+C_1}$
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Step-by-step Solution

How should I solve this problem?

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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

Group the terms of the equation

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$\left(p-w\right)dp=-dw$

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Learn how to solve problems step by step online. Solve the differential equation (p-w)dp+dw=0. Group the terms of the equation. Divide both sides of the equation by dw. Rewrite the differential equation. When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that p-w has the form Ax+By+C. Let's define a new variable u and set it equal to the expression.

Final answer to the problem

$p=w+\sqrt{-2w+C_1},\:p=w-\sqrt{-2w+C_1}$

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Function Plot

Plotting: $\left(p-w\right)dp+dw$

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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

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