Internal problem ID [10163]
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`]]
\[ \boxed {x -2 y+5+\left (2 x -y+4\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 1.281 (sec). Leaf size: 182
dsolve((x-2*y(x)+5)+(2*x-y(x)+4)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = 2-\frac {\left (x +1\right ) \left (c_{1}^{2} \left (-\frac {\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}{6 c_{1} \left (x +1\right )}-\frac {1}{2 c_{1} \left (x +1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}{3 c_{1} \left (x +1\right )}-\frac {1}{c_{1} \left (x +1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}\right )}{2}\right )+c_{1}^{2}\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 60.194 (sec). Leaf size: 1601
DSolve[(x-2*y[x]+5)+(2*x-y[x]+4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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