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2017
This chapter begins by proving the fundamental theorem on first-order ordinary differential equations in normal form, and by studying the differentiability of the solution. As a next step, it derives the canonical form of linear second-order ordinary differential equations with variable coefficients, which is very useful for qualitative investigations.
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This chapter begins by proving the fundamental theorem on first-order ordinary differential equations in normal form, and by studying the differentiability of the solution. As a next step, it derives the canonical form of linear second-order ordinary differential equations with variable coefficients, which is very useful for qualitative investigations.
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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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Remarks on the Linearization of Differential Equations
IMA Journal of Applied Mathematics, 1977openaire +2 more sources
1967
In this section we consider the vector equation $$ \mathop x\limits^. {\rm{ }} = {\rm{ }}A(t){\rm{ }}. $$ (58.1) We assume that the elements a i k (t) of the matrix A are continuous functions of t defined for t ≥ t0. Equations with a constant A, treated in sec. 4, are special cases of (58.1). On the other hand, (58.1) is a special case of the
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In this section we consider the vector equation $$ \mathop x\limits^. {\rm{ }} = {\rm{ }}A(t){\rm{ }}. $$ (58.1) We assume that the elements a i k (t) of the matrix A are continuous functions of t defined for t ≥ t0. Equations with a constant A, treated in sec. 4, are special cases of (58.1). On the other hand, (58.1) is a special case of the
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On meromorphic solutions of non-linear differential equations of Tumura–Clunie type
Mathematische Nachrichten, 2021Latreuch Zinelaabidine +1 more
exaly
Differential Equations: Linearity vs. Nonlinearity
SIAM Review, 1963Hale, J. K., LaSalle, J. P.
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