Internal problem ID [1932]
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: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y-\left (2 x +y-1\right ) y^{\prime }=-x -2} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 377
dsolve((x+2*y(x)+2)=(2*x+y(x)-1)*diff(y(x),x),y(x), singsol=all)
\[ y = -\frac {5}{3}+\frac {12 \left (3 x -4\right ) \left (-\frac {\left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{12}-\frac {1}{12 \left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}-\frac {5}{6}+\frac {i \sqrt {3}\, \left (\frac {\left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{6}-\frac {1}{6 \left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )}{2}\right )}{-3 \left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}-\frac {3}{\left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}+6+18 i \sqrt {3}\, \left (\frac {\left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}{6}-\frac {1}{6 \left (1-54 \left (3 x -4\right )^{2} c_{1} +6 \sqrt {81 \left (3 x -4\right )^{4} c_{1}^{2}-3 \left (3 x -4\right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 60.167 (sec). Leaf size: 1687
DSolve[(x+2*y[x]+2)==(2*x+y[x]-1)*y'[x],y[x],x,IncludeSingularSolutions -> True]
Too large to display