Internal problem ID [1924]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]
\[ \boxed {\left (x -2 y+2\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 1.219 (sec). Leaf size: 151
dsolve(x+(x-2*y(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {-2 \left (2 c_{1} x^{3}+2 \sqrt {-2 \left (c_{1} x^{3}-\frac {1}{2}\right ) c_{1}^{2} x^{6}}\right )^{\frac {2}{3}} c_{1} x^{2}-\frac {\left (c_{1} x^{3}+\sqrt {-2 \left (c_{1} x^{3}-\frac {1}{2}\right ) c_{1}^{2} x^{6}}\right ) \left (1+i \sqrt {3}\right ) \left (2 c_{1} x^{3}+2 \sqrt {-2 \left (c_{1} x^{3}-\frac {1}{2}\right ) c_{1}^{2} x^{6}}\right )^{\frac {1}{3}}}{2}+c_{1}^{2} \left (i \sqrt {3}-1\right ) x^{6}}{2 \left (2 c_{1} x^{3}+2 \sqrt {-2 \left (c_{1} x^{3}-\frac {1}{2}\right ) c_{1}^{2} x^{6}}\right )^{\frac {2}{3}} x^{2} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.036 (sec). Leaf size: 445
DSolve[x+(x-2*y[x]+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,1\right ]} \\ y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,2\right ]} \\ y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,3\right ]} \\ y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,4\right ]} \\ y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,5\right ]} \\ y(x)\to \frac {x+2}{2}-\frac {1}{2 \text {Root}\left [\text {$\#$1}^6 \left (16 x^6+16 e^{12 c_1}\right )-24 \text {$\#$1}^4 x^4+8 \text {$\#$1}^3 x^3+9 \text {$\#$1}^2 x^2-6 \text {$\#$1} x+1\&,6\right ]} \\ \end{align*}