12.11 problem Ex 12

Internal problem ID [10167]

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]]

Solve \begin {gather*} \boxed {x -2 y+5+\left (2 x -y+4\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.11 (sec). Leaf size: 184

dsolve((x-2*y(x)+5)+(2*x-y(x)+4)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = 2+\frac {\left (1+x \right ) \left (-c_{1}^{2}-c_{1}^{2} \left (-\frac {\left (27 c_{1} \left (1+x \right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}\right )^{\frac {1}{3}}}{6 c_{1} \left (1+x \right )}-\frac {1}{2 c_{1} \left (1+x \right ) \left (27 c_{1} \left (1+x \right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (27 c_{1} \left (1+x \right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}\right )^{\frac {1}{3}}}{3 c_{1} \left (1+x \right )}-\frac {1}{c_{1} \left (1+x \right ) \left (27 c_{1} \left (1+x \right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (1+x \right )^{2}-1}\right )^{\frac {1}{3}}}\right )}{2}\right )\right )}{c_{1}^{2}} \]

Solution by Mathematica

Time used: 60.18 (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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