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: 0.406 (sec). Leaf size: 217
dsolve((x+2*y(x)+2)=(2*x+y(x)-1)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x -3\right ) \left (i \sqrt {3}-1\right ) \left (486 \sqrt {\left (x -\frac {4}{3}\right )^{2} c_{1} \left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_{1} \right )}+1-486 \left (x -\frac {4}{3}\right )^{2} c_{1} \right )^{\frac {2}{3}}+\left (-10 x +10\right ) \left (486 \sqrt {\left (x -\frac {4}{3}\right )^{2} c_{1} \left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_{1} \right )}+1-486 \left (x -\frac {4}{3}\right )^{2} c_{1} \right )^{\frac {1}{3}}-\left (x -3\right ) \left (1+i \sqrt {3}\right )}{i \left (486 \sqrt {\left (x -\frac {4}{3}\right )^{2} c_{1} \left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_{1} \right )}+1-486 \left (x -\frac {4}{3}\right )^{2} c_{1} \right )^{\frac {2}{3}} \sqrt {3}-i \sqrt {3}-\left (486 \sqrt {\left (x -\frac {4}{3}\right )^{2} c_{1} \left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_{1} \right )}+1-486 \left (x -\frac {4}{3}\right )^{2} c_{1} \right )^{\frac {2}{3}}+2 \left (486 \sqrt {\left (x -\frac {4}{3}\right )^{2} c_{1} \left (-\frac {1}{243}+\left (x -\frac {4}{3}\right )^{2} c_{1} \right )}+1-486 \left (x -\frac {4}{3}\right )^{2} c_{1} \right )^{\frac {1}{3}}-1} \]
✓ 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]
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