If I have this pde with boundary conditions $u(0)=u(1)=0$
$ u_{xx}+ u = 1 $
How would I solve this analytically? I have forgotten how to do this, can anyone show me? Thank you
2026-04-06 12:53:16.1775479996
Analytical solution for pde
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For the complementary solution $u_C$, substitute $u(x)=\exp(\lambda x)$. For the particular solution $u_P(x)$, substitute $u(x)=a$. The general solution will be $u(x)=u_P(x)+u_C(x)$. It will have $2$ constants, which you can determine from the boundary conditions: It will give you a system of linear equations for them.