69.1.24 problem 41

Internal problem ID [14177]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 41
Date solved : Tuesday, January 28, 2025 at 06:19:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+\left (y-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 24

dsolve((x+y(x))+(y(x)-x)*diff(y(x),x)=0,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: 0.034 (sec). Leaf size: 36

DSolve[(x+y[x])+(y[x]-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-1}{K[1]^2+1}dK[1]=-\log (x)+c_1,y(x)\right ] \]