35.4.5 problem 5

Internal problem ID [6123]
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
Date solved : Monday, January 27, 2025 at 01:36:44 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 30

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

\[ y = \frac {2 c_1 x -\sqrt {1+8 \left (x +\frac {1}{2}\right )^{2} c_1^{2}}}{2 c_1} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 55

DSolve[(x-y[x])*D[y[x],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*}