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Reducibility of Linear Differential Systems to Linear Differential Equations
Moscow University Mathematics Bulletin, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2016
In this chapter we deal with some basic facts concerning ordinary linear differential equations in the analytic domain, culminating in Fuchs’ theory on regular singular points.
Anish Deb +2 more
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In this chapter we deal with some basic facts concerning ordinary linear differential equations in the analytic domain, culminating in Fuchs’ theory on regular singular points.
Anish Deb +2 more
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1966
Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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Publisher Summary This chapter focuses on higher-order linear equations. Even for second-order linear equations, no general method of solution is available as there was for first-order equations. Formulas for general solutions can be found for certain special classes of higher-order equations.
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On Systems of Linear Differential Equations
American Journal of Mathematics, 1951with U a column vector and A and P n-square matrices. The transformation U = TU, by a unimodular matrix T is easily seen to result in an equation in U, of form (1), in which the coefficient of A is T-1AT. It is known [1] that if the elements of A and its characteristic roots are holomorphic in a closed bounded region R, then there exists a matrix T ...
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On the Meromorphic Solutions of Linear Differential Equations
Journal of Systems Science and Complexity, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solutions of Linear Differential Algebraic Equations
SIAM Review, 1998Summary: The authors show how to solve inhomogeneous linear differential algebraic systems with constant coefficients.
Mazi Shirvani, Joseph W.-H. So
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On liouvillian solutions of linear differential equations
Applicable Algebra in Engineering, Communication and Computing, 1992Let \(L(y)=0\) be a homogeneous linear differential equation and \(R(z)=0\) be the associated Riccati equation. The paper deals with the problem of finding the possible degrees of the minimal polynomial of an algebraic solution of \(R(z)=0\). Supposing that \(L(y)\) is irreducible and \(L(y)=0\) has a Liouvillian solution, the author obtains sharp ...
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On Linear Perturbation of Non-Linear Differential Equations
Canadian Journal of Mathematics, 1954In the theory of the asymptotic solution or stability of ordinary differential equations most attention has been given to linear or nearly-linear cases. Investigations in this field, starting primarily with those of Kneser(7)on the equation y″+f(x)y= 0, have by now mostly been summed up in results on the vector-matrix system dy/dx =Ay +f(y,x ...
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2001
Here we consider a so called (scalar) normal system of n ordinary linear differential equations which is a system of the form $$\left\{ {\begin{array}{*{20}{c}} {{{{x'}}_{1}} = {{a}_{{11}}}(t){{x}_{1}} + {{a}_{{12}}}(t){{x}_{2}} + ... + {{a}_{{1n}}}(t){{x}_{n}} + {{f}_{1}}(t),} \\ {{{{x'}}_{2}} = {{a}_{{21}}}(t){{x}_{1}} + {{a}_{{22}}}(t){{x}_{2}} +
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Here we consider a so called (scalar) normal system of n ordinary linear differential equations which is a system of the form $$\left\{ {\begin{array}{*{20}{c}} {{{{x'}}_{1}} = {{a}_{{11}}}(t){{x}_{1}} + {{a}_{{12}}}(t){{x}_{2}} + ... + {{a}_{{1n}}}(t){{x}_{n}} + {{f}_{1}}(t),} \\ {{{{x'}}_{2}} = {{a}_{{21}}}(t){{x}_{1}} + {{a}_{{22}}}(t){{x}_{2}} +
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2014
For linear differential equations, the structures of solution spaces are characterized and solution formulas are derived in terms of fundamental matrix solutions. The calculations of fundamental matrix solutions are studied for the constant coefficient case and the Floquet theory is presented for the periodic coefficient case.
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For linear differential equations, the structures of solution spaces are characterized and solution formulas are derived in terms of fundamental matrix solutions. The calculations of fundamental matrix solutions are studied for the constant coefficient case and the Floquet theory is presented for the periodic coefficient case.
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