## 45 Reputation

2 years, 106 days

## How do I solve second order equations an...

Maple 18

I have been studying the solutions of the equation below using Maple and Mathematica.

$\large 4a_{02}^2+4ka_{02}a_{11}+k^2a_{11}^{2}+4b_{02}^{2}+4kb_{02}b_{11}+k^{2}b_{11}^{2}=0$

Here, I want to express the solutions for k. In Maple, the solution is imaginary. As one may see below.

On the other hand, if one solves that  exact equation with Mathematica, then one has real solutions. That is,

$\large k_{1,2}=\frac{1}{a_{11}^{2}+b_{11}^{2}}2\left(-a_{02}a_{11}-b_{02}b_{11}\pm\sqrt{-a_{11}^{2}b_{02}^{2}+2a_{02}a_{11}b_{02}b_{11}-a_{02}^2b_{11}^2}\right)$

Based on the above, I have a few questions:

1. What is the correct solution for the first equation above? That is, are the solutions real or complex?

2. How may I obtain the real solutions, k_{1,2}, above using Maple?

Attached below you may find my mwfile with my doubts.

Mydoubts.mw

## How may one simplify and solve equations...

Maple

Suppose one has the following equation,

.

Based on that equation, I have two questions:

1. How may one solve it for \kappa using Maple?

2. How may we simplify it?

Ps: I have tried to use the "solve" and "simplify" commands. However, Maplesoft does not return a result but rather the same equation.

## First and second derivatives of Nth degr...

Maple

Suppose

$P(x,y)=\sum_{i+j=0}^N \alpha_{i}x^{i}y^{j}$

is a multivariable polynomial of Nth degree. How may I express the first and second derivatives of $P(x,y)$ through Maplesoft?

## Maple returns unevaluated integral...

Maple

I have been trying to integrate the following an expression using Maple's command PathInt:

PathInt(4*x*y*(y^4+2*x*y-2)/sqrt((1-(2*x*y)^2+(-3*y^2+1)^2)*(1+(y^2-1)^2)), [x, y] = Path(<,>(-(1+sqrt(2))*cos(t)-(sqrt(2)-1)*sin(t), cos(t)-sin(t)), t = 0 .. 2*Pi)).

However, Maple does not return a result, but rather an integral. Is there an alternative way to solve the integral above?