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- Differential equations with separable variables Step-by-Step
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How to use it?
- Differential equation:
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Equation ydx+(3x-xy+2)dy=0
- Equation y’’-9y’+20y=0
- Equation 2y'+3ycosx=-e^(-2x)(2-3cosx)*y^(-1)
- Equation y'''-3y''+2y=0
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Identical expressions
- ydx+(3x-xy+ two)dy= zero
- ydx plus (3x minus xy plus 2)dy equally 0
- ydx plus (3x minus xy plus two)dy equally zero
- ydx+3x-xy+2dy=0
- ydx+(3x-xy+2)dy=O
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Similar expressions
- ydx+(3x-xy-2)dy=0
- ydx-(3x-xy+2)dy=0
- ydx+(3x+xy+2)dy=0
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Expressions with functions
- ydx
- ydx+(2x-3y)dy=0
- ydx-(x+sqrt(x^2+y^2))dy=0
- ydx+cotxdy=0
- ydx+(xy+2x-ye^y)dy=0
- ydx+x(lnx-lny-1)dy=0
- xy
- xy'=y-xe^(y/x)
- xydx-(x^2+3y^2)dy=0
- xydx+2(x^2+2y^2)dy=0
- xy'+y=xsinx
- xy'-y=3x^4cos^2(y/x)
- dy
- dy/dx-y=e^xy^2
- dy/dx=4y-8
- dy/dx=5y
- dy/dx=ycosx/1+2y^2
- dy/dx+y^2sinx=0
Differential equation ydx+(3x-xy+2)dy=0
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The solution
You have entered
[src]
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
The answer (#2)
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$$y\left(x\right)={\it ilt}\left({{3\,g_{19164}\,\left({{d}\over{d\,
g_{19164}}}\,\mathcal{L}\left(y\left(x\right) , x , g_{19164}\right)
\right)-{{d}\over{d\,g_{19164}}}\,\mathcal{L}\left(y\left(x\right)\,
\left({{d}\over{d\,x}}\,y\left(x\right)\right) , x , g_{19164}
\right)+2\,y\left(0\right)}\over{2\,g_{19164}-2}} , g_{19164} , x
\right)$$
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)
The answer
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/ 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
Numerical answer
[src]
(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