Cauchy-Euler

Let y be the solution of the differential equation with the initial conditions given below. If $y(x = 2) = A \ln 2$, then the value of A is ________ (rounded off to 2 decimal place...

Let $y$ be the solution of the differential equation with the initial conditions given below. If $y(x=2)=A \ln 2$, then the value of $A$ is _________ (rounded off to 2 decimal plac...

Consider the second-order linear ordinary differential equation $\rm x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0, x\ge1$ with the initial conditions $\rm y(x=1)=6, \left.\frac{dy}{dx}\...

Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ an...

The general solution of the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} + y = 0$$ is

The radial displacement in a rotating disc is governed by the differential equation $$\,\,{{{d^2}u} \over {d{x^2}}} + {1 \over x}{{du} \over {dx}} - {u \over {{x^2}}} = 8x.\,\,\,$$...