Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [fundamental-solution]

Questions on fundamental solutions of an ordinary differential equation.

An ordinary differential equation of order n will in general be satisfied by n linearly independent functions known as fundamental or elementary solutions. A general solution to the differential equation may be constructed as a linear combination of the fundamental solutions, whose coefficients are constants of integration.

225 questions
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Writing $1-e^{-xy}$ as a square.

Is it possible to write $1-e^{-xy} = r(x)r(y)$ for some function $r$ where $x,y$ are positive real numbers. I was just wondering to try to express that quantity like that. I tried solving the equation by Brut force but was not able to make any…
TRUSKI
  • 1,113
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1 answer

Polynomial Division by product of two polynomials

f(x) is a polynomial, when it is divided by (x-3) it leaves remainder 15. when f(x) is divided by square of(x-1) it leaves remainder 2x+1. Find the remainder when f(x) is divided by product of two above divisors.
Ramesh Verma
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Solution of a given equation.

We need to solve that following equation for $x$ , where , $0
User9523
  • 2,094
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3 answers

Solving an equation for a give parameter.

While solving a question , I came across the following situation , we're required to find a value for $\lambda$ , from this equation : $\lambda=(1.345)(1-e^{-\lambda})$, I tried taking logs, but couldn't get through, The solution on the other hand ,…
User9523
  • 2,094
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How to find the fundamental solution of nonhomogeneous linear second order differential equation?

I have a second-order nonhomogeneous linear differential equation, and its solution satisfies: \begin{alignat}{10} y(1)&{}={}& c_1x^2 & & &{}+{}& c*\cos x\\ y(2)&{}={}& c_2x^2 &{}-{}& c_3x &{}+{}& c*\cos x\\ y(3)&{}={}& x^2 &{}-{}& c_4x &{}+{}&…
Sht