Internal problem ID [10658]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: 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
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Abel, `2nd type`, `class A`]]
\[ \boxed {y y^{\prime }-y=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 82
dsolve(y(x)*diff(y(x),x)-y(x)=A*(exp(2*x/A)-1),y(x), singsol=all)
\[ c_{1} +2 A \arctan \left (\frac {A -y \left (x \right )}{y \left (x \right ) \sqrt {\frac {{\mathrm e}^{\frac {2 x}{A}} A^{2}-\left (A -y \left (x \right )\right )^{2}}{y \left (x \right )^{2}}}}\right )+2 y \left (x \right ) \sqrt {\frac {{\mathrm e}^{\frac {2 x}{A}} A^{2}-\left (A -y \left (x \right )\right )^{2}}{y \left (x \right )^{2}}} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y[x]*y'[x]-y[x]==A*(Exp[2*x/A]-1),y[x],x,IncludeSingularSolutions -> True]
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