Recent questions tagged initial-and-boundary-value-problems

The differential equation $\dfrac{d^{2}y}{dx^{2}}+16y=0$ for $y(x)$ with the two boundary conditions $\dfrac{dy}{dx}\bigg \vert _{x=0}=1$ and $\dfrac{dy}{dx}\bigg \vert_{...

The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________Here, $\overline{F...

The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\G...

The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________

If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .

The solution to the differential equation $\dfrac{d^2u}{dx^2}-k\dfrac{du}{dx}=0$ where $k$ is a constant, subjected to theboundary conditions $u(0)$ = $0$ and $u(L)$ = $...