Internal problem ID [1017]
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: 42.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 x +y+1}{x +2 y-4}=0} \]
✓ Solution by Maple
Time used: 4.359 (sec). Leaf size: 138
dsolve(diff(y(x),x)=(2*x+y(x)+1)/(x+2*y(x)-4),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x +5\right ) \operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}+16 c_{1} x^{3}+48 c_{1} x^{2}+64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}-8 c_{1} x^{3}-24 c_{1} x^{2}-32 c_{1} x -16 c_{1} \right )^{4}-2-x}{\operatorname {RootOf}\left (\textit {\_Z}^{16}+\left (2 c_{1} x^{4}+16 c_{1} x^{3}+48 c_{1} x^{2}+64 c_{1} x +32 c_{1} \right ) \textit {\_Z}^{4}-c_{1} x^{4}-8 c_{1} x^{3}-24 c_{1} x^{2}-32 c_{1} x -16 c_{1} \right )^{4}} \]
✓ Solution by Mathematica
Time used: 60.312 (sec). Leaf size: 8077
DSolve[y'[x]==(2*x+y[x]+1)/(x+2*y[x]-4),y[x],x,IncludeSingularSolutions -> True]
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