61.22.24 problem 24

Internal problem ID [12349]
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. subsection 1.3.1-2. Solvable equations and their solutions
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 07:55:54 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime } y-y&=-\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 270

dsolve(y(x)*diff(y(x),x)-y(x)=-12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2*x^(-1/2)),y(x), singsol=all)
 

\[ \frac {\left (3 A -\sqrt {x}\right ) \left (36 A^{4}+120 A^{3} \sqrt {x}-80 A \,x^{{3}/{2}}+52 A^{2} x +84 A^{2} y+140 A \sqrt {x}\, y+16 x^{2}-56 x y+49 y^{2}\right ) y}{8 \left (\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y}{6 A^{2}-2 A \sqrt {x}+y}\right )^{{3}/{2}} \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y}}\, \left (6 A^{2}-2 A \sqrt {x}+y\right )^{3} A}+\frac {\left (-54 A^{2}-6 A \sqrt {x}+8 x -21 y\right ) \sqrt {-\frac {\left (3 A -\sqrt {x}\right )^{2}}{6 A^{2}-2 A \sqrt {x}+y}}}{\sqrt {\frac {15 A^{2}+4 A \sqrt {x}-3 x +7 y}{6 A^{2}-2 A \sqrt {x}+y}}\, \left (36 A^{2}-12 A \sqrt {x}+6 y\right )}+c_{1} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*D[y[x],x]-y[x]==-12/49*x+2/49*A*(5*x^(1/2)+34*A+15*A^2*x^(-1/2)),y[x],x,IncludeSingularSolutions -> True]
 

Not solved