15.2.2 problem 2

Internal problem ID [2872]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 2
Date solved : Monday, January 27, 2025 at 06:21:19 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 24

dsolve((x+y(x))*diff(y(x),x)+x=y(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: 0.034 (sec). Leaf size: 34

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

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