66.1.20 problem Problem 28

Internal problem ID [13867]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 28
Date solved : Tuesday, January 28, 2025 at 06:06:11 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 y-x -4}{2 x -y+5} \end{align*}

✓ Solution by Maple

Time used: 2.518 (sec). Leaf size: 115

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

\[ y = -\frac {\left (i \sqrt {3}-1\right ) \left (27 c_{1} \left (x +2\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{{2}/{3}}-3 i \sqrt {3}-3+6 \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}+27 c_{1} x +54 c_{1} \right )^{{1}/{3}} \left (x +1\right ) c_{1}}{6 \left (27 c_{1} \left (x +2\right )+3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +2\right )^{2}-1}\right )^{{1}/{3}} c_{1}} \]

✓ Solution by Mathematica

Time used: 60.189 (sec). Leaf size: 1624

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

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