boundary-value-problem

The function $y(t)$ satisfies $$ t^2 y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0 $$ where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second derivatives of...

Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x\left( t \right) = 0$$ Given $$x(0) = 20$$ & $$\,x\left( 1 \...

A function $$n(x)$$ satisfies the differential equation $${{{d^2}n\left( x \right)} \over {d{x^2}}} - {{n\left( x \right)} \over {{L^2}}} = 0$$ where $$L$$ is a constant. The bound...

The solution of the differential equation $${k^2}{{{d^2}y} \over {d\,{x^2}}} = y - {y_2}\,\,$$ under the boundary conditions (i) $$y = {y_1}$$ at $$x=0$$ and (ii) $$y = {y_2}$$ at...

For the differential equation $${{{d^2}y} \over {d{x^2}}} + {k^2}y = 0,$$ the boundary conditions are (i) $$y=0$$ for $$x=0$$ and (ii) $$y=0$$ for $$x=a$$ The form of non-zero solu...