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Method and examples
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Method
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Solve numerical differential equation using Euler method (2nd order derivative) |
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`y''=f(x,y,z(=y'))`
=
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x0 =
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y0 =
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y'0 = z0 =
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xn =
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Step value (h) =
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Find
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Runge-Kutta Formula
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- `y'=-4z-4y`
x0 = 0, y0 = 0
z0 = 1
xn = 0.1
Step value (h) = 0.1
- `y'=1+2xy-x^2z`
x0 = 0, y0 = 1
z0 = 0
xn = 0.1
Step value (h) = 0.1
- `y'=xz^2-y^2`
x0 = 0, y0 = 1
z0 = 0
xn = 0.2
Step value (h) = 0.2
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Decimal Place =
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Trigonometry Function Mode =
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Solution
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Solution provided by AtoZmath.com
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Solve numerical differential equation using Euler method (2nd order derivative) calculator
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 1. Find y(1) for `y''=-4z-4y`, `x_0=0, y_0=0, z_0=1`, with step length 0.1
2. Find y(0.1) for `y''=1+2xy-x^2z`, `x_0=0, y_0=1, z_0=0`, with step length 0.1
3. Find y(0.2) for `y''=xz^2-y^2`, `x_0=0, y_0=1, z_0=0`, with step length 0.2
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Input functions
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Function |
Input value |
| 1. |
`x^3` |
x^3 |
| 2. |
`sqrt(x)` |
sqrt(x) |
| 3. |
`root(3)(x)`
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root(3,x)
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| 4. |
sin(x) |
sin(x) |
| 5. |
cos(x) |
cos(x) |
| 6. |
tan(x) |
tan(x) |
| 7. |
sec(x) |
sec(x) |
| 8. |
cosec(x) |
csc(x) |
| 9. |
cot(x) |
cot(x) |
| 10. |
`sin^(-1)(x)` |
asin(x) |
| 11. |
`cos^(-1)(x)` |
acos(x) |
| 12. |
`tan^(-1)(x)` |
atan(x) |
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`sin^2(x)` |
sin^2(x) |
| 14. |
`log_y(x)` |
log(y,x) |
| 15. |
`log_10(x)` |
log(x) |
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`log_e(x)` |
ln(x) |
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`e^x` |
exp(x) or e^x |
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`e^(2x)` |
exp(2x) or e^(2x) |
| 19. |
`oo` |
inf |
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