Mister Exam

# Differential equation dy+xdx=2dx

y() =
y'() =
y''() =
y'''() =
y''''() =

from to

### The solution

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d
x + --(y(x)) = 2
dx
$$x + \frac{d}{d x} y{\left(x \right)} = 2$$
x + y' = 2
Detail solution
Given the equation:
y' = $$2 - x$$
This differential equation has the form:
y' = f(x)

It is solved by multiplying both sides of the equation by dx:
y'dx = f(x)dx, or

d(y) = f(x)dx

And by using the integrals of the both equation sides:
∫ d(y) = ∫ f(x) dx

or
y = ∫ f(x) dx

In this case,
f(x) = $$2 - x$$
Consequently, the solution will be
y = $$\int \left(2 - x\right)\, dx$$
Detailed solution of the integral
or
y = $$- \frac{x^{2}}{2} + 2 x$$ + C1
where C1 is constant, independent of x
2
x
y(x) = C1 + 2*x - --
2
$$y{\left(x \right)} = C_{1} - \frac{x^{2}}{2} + 2 x$$
Graph of the Cauchy problem
The classification
nth algebraic
separable
1st exact
1st linear
Bernoulli
1st power series
lie group
nth linear constant coeff undetermined coefficients
nth linear euler eq nonhomogeneous undetermined coefficients
nth linear constant coeff variation of parameters
nth linear euler eq nonhomogeneous variation of parameters
nth algebraic Integral
separable Integral
1st exact Integral
1st linear Integral
Bernoulli Integral
nth linear constant coeff variation of parameters Integral
nth linear euler eq nonhomogeneous variation of parameters Integral
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 24.947530863880687)
(-5.555555555555555, 44.20679012313995)
(-3.333333333333333, 58.527777777460926)
(-1.1111111111111107, 67.91049382684363)
(1.1111111111111107, 72.35493827128809)
(3.333333333333334, 71.86111111079427)
(5.555555555555557, 66.42901234536217)
(7.777777777777779, 56.0586419749918)
(10.0, 40.74999999968317)
(10.0, 40.74999999968317)
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