3
votes
2answers
39 views

Solving $4y^4 - 4x^4 + x + y = 0$ (equation system of partial derivates)

I need help solving the following equation system: $$ \frac{\partial}{\partial x} = 8xy + 4y^2 + \frac{y}{x^2 + y^2} = 0 $$ $$ \frac{\partial}{\partial y} = 8xy + 4x^2 - \frac{x}{x^2 + y^2} = 0 $$ ...
1
vote
1answer
27 views

Unable to solve system of equations in Lagrange multiplier problem.

The problem: Find the right triangular prism of given volume and least area if the base is required to be a right triangle. As for parameters of the right triangular prism, $V$ is volume, $A$ is ...
1
vote
1answer
24 views

Solve system to find critical points.

Hi I have to find the stationary points for $$f(x)= x^4+y^4-(x-y)^2.$$ So far i founded the partial derivatives for $x$ and $y$. Next step is to solve this system to get my critical points: $$ ...
0
votes
1answer
48 views

Differential Equations - Method of Undetermined Coefficients for products of polynomials and sines

Consider $y''+y= 2x \sin (x)$ I have the solution for the homogeneous equation. Now i am trying to guess a particular solution for: $2x \sin (x)$ My first guess was: $(Ax+B) \cos x + (Cx +D) \sin ...
1
vote
3answers
83 views

Find three positive numbers $x$, $y$, $z$ whose sum is $10$ such that $x^2y^2z$ is a maximum

I'm self learning from the Vector Calculus book available online in PDF form (page 88). The question is: Find three positive numbers $x$, $y$, $z$ whose sum is $10$ such that $x^2y^2z$ is a maximum. ...
7
votes
2answers
114 views

Very simple partial differential equation

I am solving $$ \frac {\partial f}{\partial x} = \frac y{x^2 + y^2} \\ \frac {\partial f}{\partial y} = \frac {-x}{x^2 +y^2} $$ As $y$ was held constant when the partial derivative with respect to ...
1
vote
1answer
58 views

On a system of PDE

I would like to know what is the set of solutions to the following PDE. I think it consists of just constants, but I need help to prove. Let $f_1(p_1,p_2)$ and $f_2(p_1,p_2)$ be two functions. The ...
0
votes
1answer
232 views

How to solve for a,b,c,d from two equations?

Need to understand how to solve the following question: You have 50 coins that add up to 1 dollar. What are the possible combinations of pennys, nickels, dimes, and quarters that will satisfy these ...