69.1.58 problem 77

Internal problem ID [14211]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 77
Date solved : Tuesday, January 28, 2025 at 06:22:08 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} \frac {x}{\left (x +y\right )^{2}}+\frac {\left (2 x +y\right ) y^{\prime }}{\left (x +y\right )^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 19

dsolve(x/(x+y(x))^2+(2*x+y(x))/(x+y(x))^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {x \left (\operatorname {LambertW}\left (c_{1} x \right )-1\right )}{\operatorname {LambertW}\left (c_{1} x \right )} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 41

DSolve[x/(x+y[x])^2+(2*x+y[x])/(x+y[x])^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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