Question

undetermined coefficents solutions with designated method

please complete circled equations

4. Find the general solution by undetermined coethcies "+4y Sr +4sin(2). cos(2) +c2 sin(2r). SOLUTION: The homogeneous solution is +4-02 does match ga so we must multiply by z. So For the particular solution, Se Ae2 which does not match h. But B cos(2z)+Csin(2) Ae Br cos(2x)+ Cr sin(2r) (Bs cos(2x) )" = 0cm(2x)-,4B sin(2x)-4B2 cos(2z), Using ()"-f'g+2f's+is", we have Ca sin(2x)Osin(2r)+4C cos(22)-4Cz sin(2r). So plugging Vo in for y, and V = c1 cos(2c) + ca sin(2z) + e2. zoos(2p " +y 6 cos(z) +4sin(x). y"-10/ + 25y = 2e. 6) (k y" + 2/ + y-3 cosh(z). y" + 4y = 8 cos2(z).

Answer 1

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