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$\frac{dy}{dx}=\sin\left(x^2\right)$

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Solution

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Final answer to the problem

$y=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$
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Step-by-step Solution

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  • Equazione differenziale esatta
  • Equazione differenziale lineare
  • Equazione differenziale separabile
  • Equazione differenziale omogenea
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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

$dy=\sin\left(x^2\right)\cdot dx$

Learn how to solve equazioni differenziali problems step by step online.

$dy=\sin\left(x^2\right)\cdot dx$

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Learn how to solve equazioni differenziali problems step by step online. dy/dx=sin(x^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: dy=a\cdot dx\to \int1dy=\int adx, where a=\sin\left(x^2\right). Solve the integral \int1dy and replace the result in the differential equation. Solve the integral \int\sin\left(x^2\right)dx and replace the result in the differential equation.

Final answer to the problem

$y=\sum_{n=0}^{\infty } \frac{{\left(-1\right)}^nx^{\left(4n+3\right)}}{\left(4n+3\right)\left(2n+1\right)!}+C_0$

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Function Plot

Plotting: $\frac{dy}{dx}-\sin\left(x^2\right)$

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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

How to improve your answer:

Similar Problems Solved

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

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

$\frac{dy}{dx}=sin\left(x^2\right)$

$\frac{dy}{dx}=y^2\sin\left(x^2\right)$

$\frac{dy}{dx}=\left(ye^{-x^2}\right)$

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

$\frac{dy}{dx}=y^2-9$

Main Topic: Equazioni differenziali

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