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A Solution Manual For
Handbook of exact solutions for ordinary diﬀerential equations. By Polyanin and Zaitsev. Second edition

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Nasser M. Abbasi

May 15, 2024 Compiled on May 15, 2024 at 4:59pm

1 Chapter 1, First-Order diﬀerential equations
2 Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power Functions
3 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.3. Equations Containing Exponential Functions
4 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.3-2. Equations with power and exponential functions
5 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.4-1. Equations with hyperbolic sine and cosine
6 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.4-2. Equations with hyperbolic tangent and cotangent.
7 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-1. Equations Containing Logarithmic Functions
8 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.5-2
9 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-1. Equations with sine
10 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-2. Equations with cosine.
11 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-3. Equations with tangent.
12 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-4. Equations with cotangent.
13 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.6-5. Equations containing combinations of trigonometric functions.
14 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-1. Equations containing arcsine.
15 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-2. Equations containing arccosine.
16 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-3. Equations containing arctangent.
17 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-4. Equations containing arccotangent.
18 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.7-3. Equations containing arctangent.
19 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary functions (but not containing their derivatives).
20 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-2. Equations containing arbitrary functions and their derivatives.
21 Chapter 1, section 1.2. Riccati Equation. subsection 1.2.9. Some Transformations
22 Chapter 1, section 1.3. Abel Equations of the Second Kind. Form \(y y'-y=f(x)\). subsection 1.3.1-2. Solvable equations and their solutions
23 Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.2. Equations of the form \(y y'=f(x) y+1\)
24 Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.3-2. Equations of the form \(y y'=f_1(x) y+f_0(x)\)
25 Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.4-2. Equations of the form \((g_1(x)+g_0(x))y'=f_2(x) y^2+f_1(x) y+f_0(x)\)
26 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2 Equations Containing Power Functions. page 213
27 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-2 Equation of form \(y''+f(x)y'+g(x)y=0\)
28 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-3 Equation of form \((a x + b)y''+f(x)y'+g(x)y=0\)
29 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-4 Equation of form \(x^2 y''+f(x)y'+g(x)y=0\)
30 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-5 Equation of form \((a x^2+b x+c) y''+f(x)y'+g(x)y=0\)
31 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-6 Equation of form \((a_3 x^3+a_2 x^2 x+a_1 x+a_0) y''+f(x)y'+g(x)y=0\)
32 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-7 Equation of form \((a_4 x^4+a_3 x^3+a_2 x^2 x+a_1 x+a_0) y''+f(x)y'+g(x)y=0\)
33 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.2-8. Other equations.
34 Chapter 2, Second-Order Diﬀerential Equations. section 2.1.3-1. Equations with exponential functions