- #1
momen salah
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Homework Statement
solve using power series:
(x^2)(y")+y=0
Homework Equations
The Attempt at a Solution
after solving it i stopped at :
an[n^2-n+1]=0
Solve Power Series: (x^2)(y") + y = 0
- Thread starter momen salah
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SUMMARY
The differential equation (x^2)(y") + y = 0 is singular at x=0, making it impossible to expand in a power series around this point. To solve it using power series, one must shift the expansion point. By substituting u = x + 1, the equation transforms into (u-1)^2*y'' + y = 0, allowing for a valid power series expansion around u. This method effectively circumvents the singularity issue at x=0.
PREREQUISITES- Understanding of differential equations, specifically second-order linear equations.
- Familiarity with power series and their convergence properties.
- Knowledge of substitution methods in solving differential equations.
- Basic calculus, including differentiation and series expansion techniques.
- Study the method of power series solutions for differential equations.
- Learn about singular points in differential equations and their implications.
- Explore substitution techniques in solving differential equations.
- Investigate the convergence of power series and their applications in differential equations.
Students and educators in mathematics, particularly those focusing on differential equations and power series methods. This discussion is beneficial for anyone looking to deepen their understanding of solving singular differential equations.
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