# Tagged Questions

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

I need help solving the following equation system: $$\frac{\partial}{\partial x} = 8xy + 4y^2 + \frac{y}{x^2 + y^2} = 0$$ $$\frac{\partial}{\partial y} = 8xy + 4x^2 - \frac{x}{x^2 + y^2} = 0$$ ...
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### 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 ...
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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: $$... 1answer 48 views ### Differential Equations - Method of Undetermined Coefficients for products of polynomials and sines Consider y''+y= 2x \sin (x) I have the solution for the homogeneous equation. Now i am trying to guess a particular solution for: 2x \sin (x) My first guess was: (Ax+B) \cos x + (Cx +D) \sin ... 3answers 83 views ### Find three positive numbers x, y, z whose sum is 10 such that x^2y^2z is a maximum I'm self learning from the Vector Calculus book available online in PDF form (page 88). The question is: Find three positive numbers x, y, z whose sum is 10 such that x^2y^2z is a maximum. ... 2answers 114 views ### Very simple partial differential equation I am solving$$ \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 ...
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 ...