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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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Example1. Find y(0.2) for `y'=(x-y)/2`, y(0) = 1, with step length 0.1 using Euler method
Solution:
Given `y'=(x-y)/2, y(0)=1, h=0.1, y(0.2)=?`
Euler method
`y_1=y_0+hf(x_0,y_0)=1+(0.1)f(0,1)=1+(0.1)*(-0.5)=1+(-0.05)=0.95`
`y_2=y_1+hf(x_1,y_1)=0.95+(0.1)f(0.1,0.95)=0.95+(0.1)*(-0.425)=0.95+(-0.0425)=0.9075`
`:.y(0.2)=0.9075`
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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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