1. The problem statement, all variables and given/known data Solve the given BVP or show that it has no solution. (It does have a solution) y"+2y = x, y(0)=y([itex]\pi[/itex])=0 2. Relevant equations Characteristic polynomial is r^2 + 2 = 0. μ = √2 3. The attempt at a solution The solution to the complementary homogeneous equation is y_h = c1 cos(√2x) + c2 sin(√2x) Since the BVP is not homogeneous, there is a solution for the nonhomogeneous part. Let's call it y_c = d1*x + d2. Upon substituting into the problem, d1=1/2 and d2=0. The solution is of the form y = c1 cos(√2x) + c2 sin(√2x) + (1/2)x This was the way a similar problem was solved in the textbook. Same boundary conditions but the eqn was y"+y=x instead of y"+2y=x The solution on the back is of the form y = c1*sin(√2x) + c2*x*sin(√2x). Why is that?