(a) You are given that two solutions of the homogeneous Euler-Cauchy equation, are y = x...

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(a) You are given that two solutions of the homogeneous Euler-Cauchy equation, are y₁ = x -2 and y2 W = = x² Confirm the linear independence of your two solutions (for x > 0) by computing their Wronskian, 2² ( 1¹²2 v(z)) + = ( + y(x)) – 4 y(x)=0, z>0, 22 x (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, (i) First, enter your expression for 2² (1²2 v(2)) + 2 ( √ v (2)) – 4y (2) = − 12, z>0. dx d u(x) (as defined in lectures) below: (a) You are given that two solutions of the homogeneous Euler-Cauchy equation, are y₁ = x -2 and y2 W = = x² Confirm the linear independence of your two solutions (for x > 0) by computing their Wronskian, 2² ( 1¹²2 v(z)) + = ( + y(x)) – 4 y(x)=0, z>0, 22 x (b) Use variation of parameters to find a particular solution of the inhomogeneous Euler-Cauchy equation, (i) First, enter your expression for 2² (1²2 v(2)) + 2 ( √ v (2)) – 4y (2) = − 12, z>0. dx d u(x) (as defined in lectures) below:

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a To confirm the linear independence of the two solutions of the ... View the full answer