Internal problem ID [1016]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-6 x +y-3}{2 x -y-1}=0} \]
✓ Solution by Maple
Time used: 1.422 (sec). Leaf size: 99
dsolve(diff(y(x),x)=(-6*x+y(x)-3)/(2*x-y(x)-1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\operatorname {RootOf}\left (\textit {\_Z}^{25}+\left (-5 c_{1} x^{5}-25 c_{1} x^{4}-50 c_{1} x^{3}-50 c_{1} x^{2}-25 c_{1} x -5 c_{1} \right ) \textit {\_Z}^{5}-c_{1} x^{5}-5 c_{1} x^{4}-10 c_{1} x^{3}-10 c_{1} x^{2}-5 c_{1} x -c_{1} \right )^{20}+3 c_{1} x \left (x +1\right )^{4}}{c_{1} \left (x +1\right )^{4}} \]
✓ Solution by Mathematica
Time used: 60.095 (sec). Leaf size: 3011
DSolve[y'[x]==(-6*x+y[x]-3)/(2*x-y[x]-1),y[x],x,IncludeSingularSolutions -> True]
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