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Solve the differential equation $y^{\prime}=\frac{x-y+1}{x+y-3}$

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$yx+\frac{1}{2}y^2-3y=\frac{1}{2}x^2+x+C_0$
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 Step-by-step Solution 

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Rewrite the differential equation using Leibniz notation

$\frac{dy}{dx}=\frac{x-y+1}{x+y-3}$

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

$\frac{dy}{dx}=\frac{x-y+1}{x+y-3}$

Learn how to solve differential equations problems step by step online. Solve the differential equation y^'=(x-y+1)/(x+y+-3). Rewrite the differential equation using Leibniz notation. Rewrite the differential equation in the standard form M(x,y)dx+N(x,y)dy=0. The differential equation x+y-3dy-\left(x-y+1\right)dx=0 is exact, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and they satisfy the test for exactness: \displaystyle\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. In other words, their second partial derivatives are equal. The general solution of the differential equation is of the form f(x,y)=C. Using the test for exactness, we check that the differential equation is exact.

$yx+\frac{1}{2}y^2-3y=\frac{1}{2}x^2+x+C_0$

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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

SnapXam A2

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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

Main Topic: Differential Equations

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

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