77.1.10 problem 21 (page 30)

Internal problem ID [17900]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 21 (page 30)
Date solved : Tuesday, January 28, 2025 at 11:11:39 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y\right ) y^{\prime }&=y-x \end{align*}

✓ Solution by Maple

Time used: 0.071 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 34

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

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