Suppose L(y) = (1-x)y - 2xy + 4y. We can check that y(x) = x is...

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Suppose L(y) = (1-x²)y" - 2xy + 4y. We can check that y₁(x) = x² is a solution to L(3₁) = 2-22² (not necessary to show this). We can also check that y2(2) = x is a solution to L(y₂) = 2x. (not necessary to show this). Use linearity to determine the solution to L(y3)2-2x2x² Note that L(y) is the same operator for all the above. Suppose L(y) = (1-x²)y" - 2xy + 4y. We can check that y₁(x) = x² is a solution to L(3₁) = 2-22² (not necessary to show this). We can also check that y2(2) = x is a solution to L(y₂) = 2x. (not necessary to show this). Use linearity to determine the solution to L(y3)2-2x2x² Note that L(y) is the same operator for all the above.

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Given that Ly1xy 2xy 4y Yx x is a solution to Ly2 2x y2xx is a solution to Ly 2x N... View the full answer