Internal problem ID [4779]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR
FIRST-ORDER EQUATIONS. page 406
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (x -y\right ) y^{\prime }+y=-1-x} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 30
dsolve((x-y(x))*diff(y(x),x)+(y(x)+x+1)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 c_{1} x -\sqrt {1+8 \left (x +\frac {1}{2}\right )^{2} c_{1}^{2}}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 55
DSolve[(x-y[x])*y'[x]+(y[x]+x+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-i \sqrt {-2 x^2-2 x-c_1} \\ y(x)\to x+i \sqrt {-2 x^2-2 x-c_1} \\ \end{align*}