4.5 problem 5

Internal problem ID [4271]

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]]

Solve \begin {gather*} \boxed {\left (x -y\right ) y^{\prime }+1+x +y=0} \end {gather*}

Solution by Maple

Time used: 0.625 (sec). Leaf size: 36

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

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

Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 51

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