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$y=x^4\frac{dy}{dx}$

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Solution

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Final answer to the problem

$y=\sqrt{2\left(\frac{x^{5}}{5}+C_0\right)},\:y=-\sqrt{2\left(\frac{x^{5}}{5}+C_0\right)}$
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Step-by-step Solution

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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

$y\cdot dy=x^4dx$

Impara online a risolvere i problemi di equazioni differenziali passo dopo passo.

$y\cdot dy=x^4dx$

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Impara online a risolvere i problemi di equazioni differenziali passo dopo passo. y=x^4dy/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. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=x^4, b=y, dyb=dxa=y\cdot dy=x^4dx, dyb=y\cdot dy and dxa=x^4dx. Solve the integral \int ydy and replace the result in the differential equation. Solve the integral \int x^4dx and replace the result in the differential equation.

Final answer to the problem

$y=\sqrt{2\left(\frac{x^{5}}{5}+C_0\right)},\:y=-\sqrt{2\left(\frac{x^{5}}{5}+C_0\right)}$

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Function Plot

Plotting: $y-x^4\left(\frac{dy}{dx}\right)$

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0
a
b
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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:

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Main Topic: Equazioni differenziali

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