15.3.4 problem 4

Internal problem ID [2897]
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 : 4
Date solved : Monday, January 27, 2025 at 06:27:54 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -y+2+\left (x +y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 34

dsolve((x-y(x)+2)+(x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {3}{2}+\tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (2 x +1\right )+2 c_1 \right )\right ) \left (-x -\frac {1}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 63

DSolve[(x-y[x]+2)+(x+y[x]-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-x-2}{y(x)+x-1}\right )+\log \left (\frac {2 x^2+2 y(x)^2-6 y(x)+2 x+5}{(2 x+1)^2}\right )+2 \log (2 x+1)+c_1=0,y(x)\right ] \]