15.3.1 problem 1

Internal problem ID [2894]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 1
Date solved : Monday, January 27, 2025 at 06:27:42 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 32

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

\[ y = 1+\tan \left (\operatorname {RootOf}\left (2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x +1\right )+2 c_1 \right )\right ) \left (-x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 56

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

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