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4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).

4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).
Transcribed Image Text:4. Make up an ODE with desired solutions: a) The following equation has been "rigged" to have "1/x" and "1/(1-x)" as solutions. Solve the following equation by the method of Frobenius, and show that you do indeed obtain those solutions. (x²-x)y "+(4x-2)y '+2y=0 (0 < x <1) b) Please make up a linear homogeneous second-order ODE that has two prescribed LI solutions F(x) and G(x).
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