please solve Q part 1, p2, and p3 in step by step so i can follow up with you

and the prof. said this is non- liner, non- homogenius, and we have to solve it using the method of characteristics.

Thank you

P1.* Solve the following problem, and determine the values of x and y for which a solution exists: 4x + 4y = 1 - ul.r, x) = sin(x) > 0. P2.* Solve the following problem, and determine the values of r and y for which a solution exists: -yur + muy = u u(x,0) = e ER. P3. Find a solution to the wave equation oul - cru = 0 u(3,0) = f(x) ( 3,0) = 9(2) >0, reR RER PER by splitting the differential operator as: dull - zdroll = (ar - zd) (Jrlu + vall), and then applying twice the method of characteristics. P1.* Solve the following problem, and determine the values of and y for which a solution exists: Ux+ly = 1 - u u(x,x) = sin(r) r>0. P2.* Solve the following problem, and determine the values of r and y for which a solution exists: -yur + guy = 11 (,0) = e reR. P3. Find a solution to the wave equation Oull 20xxl = 0 u(x,0) = f(x) (u(x,0) = g(x) t>0, ER XER by splitting the differential operator as: dulu - parell = (at - zd) (dru + vall), and then applying twice the method of characteristics. P1.* Solve the following problem, and determine the values of x and y for which a solution exists: 4x + 4y = 1 - ul.r, x) = sin(x) > 0. P2.* Solve the following problem, and determine the values of r and y for which a solution exists: -yur + muy = u u(x,0) = e ER. P3. Find a solution to the wave equation oul - cru = 0 u(3,0) = f(x) ( 3,0) = 9(2) >0, reR RER PER by splitting the differential operator as: dull - zdroll = (ar - zd) (Jrlu + vall), and then applying twice the method of characteristics. P1.* Solve the following problem, and determine the values of and y for which a solution exists: Ux+ly = 1 - u u(x,x) = sin(r) r>0. P2.* Solve the following problem, and determine the values of r and y for which a solution exists: -yur + guy = 11 (,0) = e reR. P3. Find a solution to the wave equation Oull 20xxl = 0 u(x,0) = f(x) (u(x,0) = g(x) t>0, ER XER by splitting the differential operator as: dulu - parell = (at - zd) (dru + vall), and then applying twice the method of characteristics