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Solve the differential equation $6y\sin\left(y^2\right)\cdot dy=4x\cos\left(x\right)\cdot dx$

Step-by-step Solution

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Solution

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Final answer to the problem

$-3\cos\left(y^2\right)=4x\sin\left(x\right)+4\cos\left(x\right)+C_0$
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Step-by-step Solution

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Learn how to solve integration by parts problems step by step online. Solve the differential equation 6ysin(y^2)dy=4xcos(x)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int6y\sin\left(y^2\right)dy and replace the result in the differential equation. Solve the integral \int4x\cos\left(x\right)dx and replace the result in the differential equation.

Final answer to the problem

$-3\cos\left(y^2\right)=4x\sin\left(x\right)+4\cos\left(x\right)+C_0$

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Function Plot

Plotting: $6y\sin\left(y^2\right)\cdot dy-4x\cos\left(x\right)\cdot dx$

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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

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$\frac{dy}{dx}=\sin5x$

$\frac{dy}{dx}=\frac{x^2-y^2}{3xy}$

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

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

Main Topic: Integration by Parts

Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.

Used Formulas

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