78.8.30 problem 30

Internal problem ID [18228]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 30
Date solved : Tuesday, January 28, 2025 at 11:42:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +2 y+2}{-2 x +y} \end{align*}

✓ Solution by Maple

Time used: 0.291 (sec). Leaf size: 30

dsolve(diff(y(x),x)=(x+2*y(x)+2)/(-2*x+y(x)),y(x), singsol=all)
 

\[ y = \frac {10 c_{1} x -\sqrt {1+125 \left (x +\frac {2}{5}\right )^{2} c_{1}^{2}}}{5 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 59

DSolve[D[y[x],x]==(x+2*y[x]+2)/(-2*x+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 x-i \sqrt {-5 x^2-4 x-c_1} \\ y(x)\to 2 x+i \sqrt {-5 x^2-4 x-c_1} \\ \end{align*}