Browsing by Author "Befikadu Aregahegn"

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    On Riccati Equations and their Analytic Solutions
    (Addis Ababa University, 2025-08) Befikadu Aregahegn; Tesfa Biset
    This thesis, "On Riccati Equations and Their Analytic Solutions," examines the Riccati differential equations, a family of nonlinear equations, and their solutions. The study aims to analyze the forms and properties of Riccati equations and provide analytical solutions. Riccati equations were converted to linear or separable equations by means of analytical substitutions and transformations. Three major classes were examined. By applying integrating factors and validating specific solutions, Type One equations were resolved. Partial fractions were used to implicitly solve Type Two problems by converting them into separable forms. Explicit answers were obtained by reducing Type Three equations to first-order linear forms. The findings demonstrate that analytical techniques offer precise, insightful and effective answers.
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    On Riccati Equations and their Analytic Solutions
    (Addis Ababa University, 2025-08) Befikadu Aregahegn; Tesfa Biset
    This thesis, "On Riccati Equations and Their Analytic Solutions," examines the Riccati differential equations, a family of nonlinear equations, and their solutions. The study aims to analyze the forms and properties of Riccati equations and provide analytical solutions. Riccati equations were converted to linear or separable equations by means of analytical substitutions and transformations. Three major classes were examined. By applying integrating factors and validating specific solutions, Type One equations were resolved. Partial fractions were used to implicitly solve Type Two problems by converting them into separable forms. Explicit answers were obtained by reducing Type Three equations to first-order linear forms. The findings demonstrate that analytical techniques offer precise, insightful and effective answers.
  • No Thumbnail Available
    Item
    On Riccati Equations and their Analytic Solutions
    (Addis Ababa University, 2025-08) Befikadu Aregahegn; Tesfa Biset
    This thesis, "On Riccati Equations and Their Analytic Solutions," examines the Riccati differential equations, a family of nonlinear equations, and their solutions. The study aims to analyze the forms and properties of Riccati equations and provide analytical solutions. Riccati equations were converted to linear or separable equations by means of analytical substitutions and transformations. Three major classes were examined. By applying integrating factors and validating specific solutions, Type One equations were resolved. Partial fractions were used to implicitly solve Type Two problems by converting them into separable forms. Explicit answers were obtained by reducing Type Three equations to first-order linear forms. The findings demonstrate that analytical techniques offer precise, insightful and effective answers.