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$\frac{dy}{dx}=\frac{x-5}{y^2}$

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Solution

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Final answer to the problem

$y=\sqrt[3]{3\left(\frac{x^2}{2}-5x+C_0\right)}$
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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

$y^2dy=\left(x-5\right)dx$

Learn how to solve calcul différentiel problems step by step online.

$y^2dy=\left(x-5\right)dx$

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Learn how to solve calcul différentiel problems step by step online. dy/dx=(x-5)/(y^2). 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-5, b=y^2, dyb=dxa=y^2dy=\left(x-5\right)dx, dyb=y^2dy and dxa=\left(x-5\right)dx. Expand the integral \int\left(x-5\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Solve the integral \int y^2dy and replace the result in the differential equation.

Final answer to the problem

$y=\sqrt[3]{3\left(\frac{x^2}{2}-5x+C_0\right)}$

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Function Plot

Plotting: $\frac{dy}{dx}+\frac{-x+5}{y^2}$

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7
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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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