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Solve the differential equation $y^{\prime}=\sin\left(x+y-1\right)^2$

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Solution

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Final answer to the problem

$\frac{6\tan\left(\frac{x+y-1}{2}\right)+2\tan\left(\frac{x+y-1}{2}\right)^{3}}{3\left(y^2+6y+1\right)}=x+C_0$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Rewrite the differential equation using Leibniz notation

Learn how to solve differential equations problems step by step online.

$\frac{dy}{dx}=\sin\left(x+y-1\right)^2$

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Unlock the first 3 steps of this solution

Learn how to solve differential equations problems step by step online. Solve the differential equation y^'=sin(x+y+-1)^2. Rewrite the differential equation using Leibniz notation. When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that x+y-1 has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable y. Differentiate both sides of the equation with respect to the independent variable x.

Final answer to the problem

$\frac{6\tan\left(\frac{x+y-1}{2}\right)+2\tan\left(\frac{x+y-1}{2}\right)^{3}}{3\left(y^2+6y+1\right)}=x+C_0$

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Function Plot

Plotting: $\frac{6\tan\left(\frac{x+y-1}{2}\right)+2\tan\left(\frac{x+y-1}{2}\right)^{3}}{3\left(y^2+6y+1\right)}=x+C_0$

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m
n
u
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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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$\frac{dx}{dy}=sin\left(x-y-1\right)$

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

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

See formulas (4)

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