40.3.8 problem 23 (m)

Internal problem ID [6612]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 23 (m)
Date solved : Monday, January 27, 2025 at 02:15:53 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y+1-\left (y-x +3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.094 (sec). Leaf size: 30

dsolve((x+y(x)+1)-(y(x)-x+3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-\sqrt {2 \left (x -1\right )^{2} c_1^{2}+1}+\left (x -3\right ) c_1}{c_1} \]

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 59

DSolve[(x+y[x]+1)-(y[x]-x+3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {-2 x^2+4 x-9-c_1}+x-3 \\ y(x)\to i \sqrt {-2 x^2+4 x-9-c_1}+x-3 \\ \end{align*}