56.1.39 problem 40

Internal problem ID [8751]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 40
Date solved : Monday, January 27, 2025 at 04:46:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime } y-y&=x \end{align*}

✓ Solution by Maple

Time used: 0.327 (sec). Leaf size: 53

dsolve(y(x)*diff(y(x),x)-y(x)=x,y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {-x^{2}-x y+y^{2}}{x^{2}}\right )}{2}-\frac {\sqrt {5}\, \operatorname {arctanh}\left (\frac {\left (x -2 y\right ) \sqrt {5}}{5 x}\right )}{5}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 63

DSolve[y[x]*D[y[x],x] - y[x] == x,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{10} \left (\left (5+\sqrt {5}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {5}+1\right )-\left (\sqrt {5}-5\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {5}-1\right )\right )=-\log (x)+c_1,y(x)\right ] \]