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Solve the differential equation $\sqrt{y^2+1}dx=xy\cdot dy$

Step-by-step Solution

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Final Answer

$\sqrt{y^2+1}=\ln\left(x\right)+C_0$
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Step-by-step Solution

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Divide fractions $\frac{1}{\frac{\sqrt{y^2+1}}{y}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

$\frac{y}{\sqrt{y^2+1}}=\frac{1}{x}$

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$\frac{y}{\sqrt{y^2+1}}=\frac{1}{x}$

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Learn how to solve problems step by step online. Solve the differential equation (y^2+1)^1/2dx=xydy. Divide fractions \frac{1}{\frac{\sqrt{y^2+1}}{y}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Integrate both sides of the differential equation, the left side with respect to . Solve the integral \int\frac{y}{\sqrt{y^2+1}}dy and replace the result in the differential equation. Solve the integral \int\frac{1}{x}dx and replace the result in the differential equation.

Final Answer

$\sqrt{y^2+1}=\ln\left(x\right)+C_0$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $\sqrt{y^2+1}dx-xy\cdot dy$

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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
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

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