Internal problem ID [10783]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 y-x -4}{2 x -y+5}=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 184
dsolve(diff(y(x),x)=(2*y(x)-x-4)/(2*x-y(x)+5),y(x), singsol=all)
\[ y \left (x \right ) = 1+\frac {\left (x +2\right ) \left (-c_{1}^{2}-c_{1}^{2} \left (-\frac {\left (27 \left (x +2\right ) c_{1} +3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{\frac {1}{3}}}{6 c_{1} \left (x +2\right )}-\frac {1}{2 c_{1} \left (x +2\right ) \left (27 \left (x +2\right ) c_{1} +3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (27 \left (x +2\right ) c_{1} +3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{\frac {1}{3}}}{3 c_{1} \left (x +2\right )}-\frac {1}{c_{1} \left (x +2\right ) \left (27 \left (x +2\right ) c_{1} +3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{\frac {1}{3}}}\right )}{2}\right )\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 60.185 (sec). Leaf size: 628
DSolve[y'[x]==(2*y[x]-x-4)/(2*x-y[x]+5),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x+\frac {3 (x+2)}{\frac {1}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}-\frac {\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}{(x+2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-1}+5 \\ y(x)\to 2 x+\frac {6 (x+2)}{\frac {-1-i \sqrt {3}}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}{(x+2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-2}+5 \\ y(x)\to 2 x+\frac {6 (x+2)}{\frac {i \left (\sqrt {3}+i\right )}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x+2)^4+2 e^{\frac {3 c_1}{8}} (x+2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+2)^2\right ){}^3}-1}}{(x+2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-2}+5 \\ \end{align*}