Cosmo-san | is anyone here knowledgeable with Second Solutions by reduction of order? |

TRWBW | http://www.sosmath.com/diffeq/second/reduction/reduction.html |

Cosmo-san | ah, thank you |

Phylo | % Integrate[x/E^(X), x] |

mbot | Phylo: x^2/(2*E^X) |

Phylo | does case matter for x? |

excelblue | yes they even matter on paper |

Phylo | indeed it does lol, true is there a simpler way other than integration by parts to solve x/E^(x)? |

JIMJONESBALLIN | Suppose that <o,o>_1 and <o,o>_2 are two inner product spaces on a vector space V. Prove that <o,o> = <o,o>_1 + <o,o>_2 is also an inner product on V. |

TRWBW | JIMJONESBALLIN: what's the def of an innner product space? just to get it all out in the open JIMJONESBALLIN: um, inner product |

JIMJONESBALLIN | Its a Vector space over a field endowed with an inner product. |

TRWBW | JIMJONESBALLIN: so are you talking an arbitrary field or R or C or what? |

JIMJONESBALLIN | The question doesnt say. But I think its over F^n No, my apologies. Its over |R |

TRWBW | JIMJONESBALLIN: so is your problem that you don't understand the question? JIMJONESBALLIN: k |

seb-_ | % Solve[a x x + b x + c == 0, x] |

mbot | seb-_: {{x -> (-b - Sqrt[b^2 - 4*a*c])/(2*a)}, {x -> (-b + Sqrt[b^2 - 4*a*c])/(2*a)}} |

TRWBW | JIMJONESBALLIN: is your question how to solve this, or what is the definition of an inner product? |

JIMJONESBALLIN | I'm tryna prove it. |

TRWBW | JIMJONESBALLIN: what are you trying to prove? i'm asking do you know the definition of an inner product? |

Phylo | ... if x and X are different, what is E as opposed to e? |

|Steve| | So show that <-,->_1 + <-,->_2 satisfies the properties of an inner product. |

JIMJONESBALLIN | Oh sorry, I thought you asked for the definition of an inner product space. |

Phylo | and why doesn't e^f(x) work? |

TRWBW | |Steve|: i'm trying to get at that. is his problem how to show it, or that he doesn't know what the definitions involved are? |

Phylo | where E^f(x) does |

JIMJONESBALLIN | An inner product on a vs V is just a function that assigns to every ordered pair of vectors x and y in V a scalar in F denoted <x,y> |

|Steve| | Phylo: That was already answered. e is a variable, E is the base of the natural logarithm. |

TRWBW | JIMJONESBALLIN: just? |

JIMJONESBALLIN | No, more to follow. |

TRWBW | k |

dn4 | [1+2xCos(x)+sin^2(x)]/[x^2+2xCos(x)+Cos^2(x)] <-- when reducing this fraction's "2xCos(x)" Does it = [1+1+sin^2(x)]/[x^2+1+Cos^2(x)] ? |

|Steve| | It's also F-linear in the first argument, etc. |

TRWBW | |Steve|: i'm sure you know it. ;) |

JIMJONESBALLIN | such that for all x,y and z in V and all c in F we have: a) <x + z, y> = <x,y> + <z,y> |