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Other calculators
- Linear homogeneous differential equations of 2nd order Step-By-Step
- Linear inhomogeneous differential equations of the 1st order Step-By-Step
- Differential equations with separable variables Step-by-Step
- A simplest differential equations of 1-order Step-by-Step
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How to use it?
- Differential equation:
- Equation xy''-(2x+1)y'+(x+1)y=0
- Equation dy/dx=(x^2+3y^2)/(2xy)
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Equation y'+4y=1.4
- Equation xe^ydy+x^2+1/ydx=0
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Identical expressions
- xy''-(2x+ one)y'+(x+ one)y= zero
- xy two strokes of the second (2nd) order minus (2x plus 1)y stroke first (1st) order plus (x plus 1)y equally 0
- xy two strokes of the second (2nd) order minus (2x plus one)y stroke first (1st) order plus (x plus one)y equally zero
- xy''-2x+1y'+x+1y=0
- xy''-(2x+1)y'+(x+1)y=O
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Similar expressions
- xy''-(2x-1)y'+(x+1)y=0
- xy''-(2x+1)y'-(x+1)y=0
- xy''+(2x+1)y'+(x+1)y=0
- xy''-(2x+1)y'+(x-1)y=0
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Expressions with functions
- 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)
Differential equation xy''-(2x+1)y'+(x+1)y=0
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The solution
You have entered
[src]
2
d d
x*---(y(x)) + (1 + x)*y(x) - (1 + 2*x)*--(y(x)) = 0
2 dx
dx
$$x \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \left(x + 1\right) y{\left(x \right)} - \left(2 x + 1\right) \frac{d}{d x} y{\left(x \right)} = 0$$
x*y'' + (x + 1)*y - (2*x + 1)*y' = 0
The answer (#2)
[src]
$$y\left(x\right)={\it ilt}\left(-{{\left(g_{19164}^2-2\,g_{19164}+1
\right)\,\left({{d}\over{d\,g_{19164}}}\,\mathcal{L}\left(y\left(x
\right) , x , g_{19164}\right)\right)-2\,y\left(0\right)}\over{3\,
g_{19164}-3}} , g_{19164} , x\right)$$
y = 'ilt(-((g19164^2-2*g19164+1)*'diff('laplace(y,x,g19164),g19164,1)-2*y(0))/(3*g19164-3),g19164,x)
The answer
[src]
/ 4 5 3\ / 2 3\
| 5*x 3*x x | 2 | x x | / 6\
y(x) = C2*|1 + x - ---- - ---- - --| + C1*x *|1 + x + -- + --| + O\x /
\ 24 40 3 / \ 2 6 /
$$y{\left(x \right)} = C_{2} \left(- \frac{3 x^{5}}{40} - \frac{5 x^{4}}{24} - \frac{x^{3}}{3} + x + 1\right) + C_{1} x^{2} \left(\frac{x^{3}}{6} + \frac{x^{2}}{2} + x + 1\right) + O\left(x^{6}\right)$$
The classification
2nd power series regular
factorable