62.12.11 problem Ex 12

Internal problem ID [12857]
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
Date solved : Tuesday, January 28, 2025 at 04:28:38 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 2.433 (sec). Leaf size: 115

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

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

✓ Solution by Mathematica

Time used: 60.186 (sec). Leaf size: 1601

DSolve[(x-2*y[x]+5)+(2*x-y[x]+4)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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