Internal problem ID [5269]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y-\left (y-x +3\right ) y^{\prime }=-x -1} \]
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 32
dsolve((x+y(x)+1)-(y(x)-x+3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -2-\frac {-\left (x -1\right ) c_{1} +\sqrt {2 \left (x -1\right )^{2} c_{1}^{2}+1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 59
DSolve[(x+y[x]+1)-(y[x]-x+3)*y'[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*}