Internal problem ID [11181]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19.
Summary. Page 29
Problem number: Ex 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-2 y+\left (2 x -y+4\right ) y^{\prime }=-x -5} \]
✓ Solution by Maple
Time used: 0.766 (sec). Leaf size: 117
dsolve((x-2*y(x)+5)+(2*x-y(x)+4)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (i \sqrt {3}-1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}+27 c_{1} \left (1+x \right )\right )^{\frac {2}{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}+27 c_{1} x +27 c_{1} \right )^{\frac {1}{3}} \left (-1+x \right ) c_{1}}{6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}+27 c_{1} \left (1+x \right )\right )^{\frac {1}{3}} c_{1}} \]
✓ Solution by Mathematica
Time used: 60.282 (sec). Leaf size: 1601
DSolve[(x-2*y[x]+5)+(2*x-y[x]+4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display