5.43 problem 42

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]]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +y+1}{x +2 y-4}=0} \end {gather*}

Solution by Maple

Time used: 0.841 (sec). Leaf size: 64

dsolve(diff(y(x),x)=(2*x+y(x)+1)/(x+2*y(x)-4),y(x), singsol=all)
 

\[ y \relax (x ) = 3+\frac {\left (2+x \right ) \left (\RootOf \left (\textit {\_Z}^{16}+2 \left (2+x \right )^{4} c_{1} \textit {\_Z}^{4}-\left (2+x \right )^{4} c_{1}\right )^{4}-1\right )}{\RootOf \left (\textit {\_Z}^{16}+2 \left (2+x \right )^{4} c_{1} \textit {\_Z}^{4}-\left (2+x \right )^{4} c_{1}\right )^{4}} \]

Solution by Mathematica

Time used: 0.309 (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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