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Solve the differential equation $\frac{dy}{dx}=4x+\frac{4x}{\sqrt{16-x^2}}$

Step-by-step Solution

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Solution

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Final Answer

$y=-2\left(16-x^2\right)-4\sqrt{16-x^2}+C_0$
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Step-by-step Solution

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Combine all terms into a single fraction with $\sqrt{16-x^2}$ as common denominator

$\frac{dy}{dx}=\frac{4x\sqrt{16-x^2}+4x}{\sqrt{16-x^2}}$

Learn how to solve integral calculus problems step by step online.

$\frac{dy}{dx}=\frac{4x\sqrt{16-x^2}+4x}{\sqrt{16-x^2}}$

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Learn how to solve integral calculus problems step by step online. Solve the differential equation dy/dx=4x+(4x)/((16-x^2)^1/2). Combine all terms into a single fraction with \sqrt{16-x^2} as common denominator. 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. Simplify the expression \frac{4x\sqrt{16-x^2}+4x}{\sqrt{16-x^2}}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final Answer

$y=-2\left(16-x^2\right)-4\sqrt{16-x^2}+C_0$

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Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $\frac{dy}{dx}-4x+\frac{-4x}{\sqrt{16-x^2}}$

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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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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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