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Method and examples
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Method
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Solve numerical differential equation using Euler method (1st order derivative) |
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`y'=f(x,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'=-2x-y`
x0 = 0, y0 = -1
xn = 0.5
Step value (h) = 0.1
- `y'=(x-y)/2`
x0 = 0, y0 = 1
xn = 0.2
Step value (h) = 0.1
- `y'=-(x*y^2+y)`
x0 = 0, y0 = 1
xn = 0.3
Step value (h) = 0.1
- `y'=-y`
x0 = 0, y0 = 1
xn = 0.2
Step value (h) = 0.1
- `y'=x-y^2`
x0 = 0, y0 = 1
xn = 0.2
Step value (h) = 0.1
- `y'=x^2-y`
x0 = 0, y0 = 1
xn = 0.2
Step value (h) = 0.1
- `y'=x^2y-1`
x0 = 0, y0 = 1
xn = 0.2
Step value (h) = 0.1
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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 (1st order derivative) calculator
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 1. Find y(0.5) for `y'=-2x-y`, y(0) = -1, with step length 0.1
2. Find y(2) for `y'=(x-y)/2`, y(0) = 1, with step length 0.2
3. Find y(0.3) for `y'=-(x*y^2+y)`, y(0) = 1, with step length 0.1
4. Find y(0.2) for `y'=-y`, y(0) = 1, with step length 0.1
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Input functions
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| Sr No. |
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) |
| 13. |
`sin^2(x)` |
sin^2(x) |
| 14. |
`log_y(x)` |
log(y,x) |
| 15. |
`log_10(x)` |
log(x) |
| 16. |
`log_e(x)` |
ln(x) |
| 17. |
`e^x` |
exp(x) or e^x |
| 18. |
`e^(2x)` |
exp(2x) or e^(2x) |
| 19. |
`oo` |
inf |
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