Empty Part only Let L[y]: y"" y'+4xy, yi (x): = sinx, y2(x): =x. Verify that L[y11(x)...
9. Superposition Principle: Let L[yl=y" + y + xy, yı(x)=sinx ^yz(x)=x.If L[y] x = xsinx and L(y2 x)=x²+1 then use the superposition principle to find a solution to the differential equation: L[y]=4x²+4-6 xsinx
4. Verify that yi xPJp(x) and y2 - xPYp(x) are linearly independent solutions of xy" + (1-2 )y, + xy-0, x > 0. 4. Verify that yi xPJp(x) and y2 - xPYp(x) are linearly independent solutions of xy" + (1-2 )y, + xy-0, x > 0.
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...