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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(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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Example1. Find y(0.1) for y''=1+2xy-x^2z, x_0=0, y_0=1, z_0=0, with step length 0.1 using Euler method (2nd order derivative)
Solution:
Given y^('')=1+2xy-x^2z, y(0)=1, y'(0)=0, h=0.1, y(0.1)=?
put (dy)/(dx)=z and differentiate w.r.t. x, we obtain (d^2y)/(dx^2)=(dz)/(dx)
We have system of equations
(dy)/(dx)=z=f(x,y,z)
(dz)/(dx)=1+2xy-x^2z=g(x,y,z)
Euler method for second order differential equation
y_1=y_0+hf(x_0,y_0,z_0)=1+(0.1)*f(0,1,0)=1+(0.1)*(0)=1+(0)=1
:.y(0.1)=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)
|
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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