15.3.5 problem 5

Internal problem ID [2898]
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 : 5
Date solved : Monday, January 27, 2025 at 06:27:57 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 35

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

\begin{align*} y &= x -1-\sqrt {2 c_1 -2 x +1} \\ y &= x -1+\sqrt {2 c_1 -2 x +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 49

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

\begin{align*} y(x)\to x-i \sqrt {2 x-1-c_1}-1 \\ y(x)\to x+i \sqrt {2 x-1-c_1}-1 \\ \end{align*}