12.5.42 problem 41

Internal problem ID [1666]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 41
Date solved : Monday, January 27, 2025 at 05:23:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \end{align*}

✓ Solution by Maple

Time used: 0.232 (sec). Leaf size: 99

dsolve(diff(y(x),x)=(-6*x+y(x)-3)/(2*x-y(x)-1),y(x), singsol=all)
 

\[ y = \frac {-\operatorname {RootOf}\left (\textit {\_Z}^{25}+\left (-5 c_1 \,x^{5}-25 c_1 \,x^{4}-50 c_1 \,x^{3}-50 c_1 \,x^{2}-25 c_1 x -5 c_1 \right ) \textit {\_Z}^{5}-c_1 \,x^{5}-5 c_1 \,x^{4}-10 c_1 \,x^{3}-10 c_1 \,x^{2}-5 c_1 x -c_1 \right )^{20}+3 x c_1 \left (x +1\right )^{4}}{c_1 \left (x +1\right )^{4}} \]

✓ Solution by Mathematica

Time used: 60.090 (sec). Leaf size: 3011

DSolve[D[y[x],x]==(-6*x+y[x]-3)/(2*x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

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