Solve the differential equation $y\cdot dy+x\cdot dx=3xy^2dx$

Step-by-step Solution

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Final answer to the problem

$y=\sqrt{C_2e^{3x^2}+\frac{1}{3}},\:y=-\sqrt{C_2e^{3x^2}+\frac{1}{3}}$
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Step-by-step Solution

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1

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $x\cdot dx$ from both sides of the equation

$y\cdot dy=3xy^2dx-x\cdot dx$

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$y\cdot dy=3xy^2dx-x\cdot dx$

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Learn how to solve differential calculus problems step by step online. Solve the differential equation ydy+xdx=3xy^2dx. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x\cdot dx from both sides of the equation. Factor the polynomial 3xy^2dx-x\cdot dx by it's greatest common factor (GCF): x\cdot dx. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final answer to the problem

$y=\sqrt{C_2e^{3x^2}+\frac{1}{3}},\:y=-\sqrt{C_2e^{3x^2}+\frac{1}{3}}$

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Function Plot

Plotting: $y\cdot dy+x\cdot dx-3xy^2dx$

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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
Dx
|◻|
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:

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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