Second order differential equations

Can someone help me with the following :
d^2y/dx^2 + d^2z/dx^2 +d^2w/dx^2 = N(x)
Where N = y + z + w

 

It looks like you have only one equation in three unknowns. Typically, in such a situation, the best you can do is solve for one unknown in terms of the other two.

 

In fact, with y+ z+ w= N, w= N- y- z so dw/dx= -dy/dx- dz/dx and d^2w/dx^2= -d^2y/dx^2- d^2z/dx^2 so d^2/dx^2+ d^2z/dx^2+ d^2w/dx^2= d^2y/dx^2+d^2z/dx^2- d^2y/dx^2- d^2z/dx^2= 0= y+ z+ w.

Any functions, y(x), z(x), w(x) that satisfy w(x)= -y(x)- z(x) will satisfy both equations!