Laplace equation:
$\frac{\partial^{2}H}{\partial\,x^2} + \frac{\partial^{2}H}{\partial\,y^2} + \frac{\partial^{2}H}{\partial\,z^2}=0$
Head $H$ doesn’t vary in $y$ and $z$ directions. Boundary conditions are : at $x=0$, $H=5$; and $\frac{dH}{dx}=−1$. What is the value of $H$ at $x=1.2$ . I have got the answer but cannot solve it. Please help me to solve this equation.
If you mean by "$H$ doesn't vary in $y$ and $z$ directions" that $H$ is constant in $y$ and $z$ direction, the whole problem simplifies to an ODE: $$ \frac{\partial ^2 H}{\partial x^2} =0 $$ Since $$ \frac{\partial H}{\partial x}=-1 $$ we get that $$ H(x,y,z)=-x+C $$ Plugging in the inital conditions, gives us: $$ H(x,y,z)=-x+5 $$