Sum

Solve `dy/dx=x.y` with help of Euler’s method ,given that y(0)=1 and find y when x=0.3

(Take h=0.1)

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#### Solution

`dy/dx=x.y=f(x,y)` `x_0=0, y_0=1`

`y_n=y_(n-1)+h.f(x_(n-1), y_(n-1))`

Iteration (n) | `x_n` | `y_n` | `f(x_n,y_y)` | `y_n+1=y_n+h.f(x_n,y_n)` |

0 | 0 | 1 | 0 | 1 |

1 | 0.1 | 1 | 0.1 | 1.01 |

2 | 0.2 | 1.01 | 0.202 | 1.0302 |

∴y(0.3)=1.0302

Concept: Euler’S Method

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