Mister Exam

# Differential equation ydx+(3x-xy+2)dy=0

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

from to

### The solution

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  d              d            d
2*--(y(x)) + 3*x*--(y(x)) - x*--(y(x))*y(x) + y(x) = 0
dx             dx           dx                      
$$- x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 3 x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} + 2 \frac{d}{d x} y{\left(x \right)} = 0$$
-x*y*y' + 3*x*y' + y + 2*y' = 0
$$y\left(x\right)={\it ilt}\left({{3\,g_{19164}\,\left({{d}\over{d\, g_{19164}}}\,\mathcal{L}\left(y\left(x\right) , x , g_{19164}\right) \right)-{{d}\over{d\,g_{19164}}}\,\mathcal{L}\left(y\left(x\right)\, \left({{d}\over{d\,x}}\,y\left(x\right)\right) , x , g_{19164} \right)+2\,y\left(0\right)}\over{2\,g_{19164}-2}} , g_{19164} , x \right)$$
y = 'ilt((3*g19164*'diff('laplace(y,x,g19164),g19164,1)-'diff('laplace(y*'diff(y,x,1),x,g19164),g19164,1)+2*y(0))/(2*g19164-2),g19164,x)
       /     2            \  -y(x)      3     -y(x)
C1 - 2*\2 + y (x) + 2*y(x)/*e      + x*y (x)*e      = 0
$$x y^{3}{\left(x \right)} e^{- y{\left(x \right)}} + C_{1} - 2 \left(y^{2}{\left(x \right)} + 2 y{\left(x \right)} + 2\right) e^{- y{\left(x \right)}} = 0$$
Graph of the Cauchy problem
The classification
1st exact
1st exact Integral
1st power series
factorable
lie group
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8519188330644439)
(-5.555555555555555, 1.0320944051712322)
(-3.333333333333333, 1.557904172757292)
(-1.1111111111111107, 2.2921385199051687)
(1.1111111111111107, 0.0)
(3.333333333333334, 0.0)
(5.555555555555557, 0.0)
(7.777777777777779, 0.0)
(10.0, 0.0)
(10.0, 0.0)
The graph
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