Internal problem ID [2171]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 \left (-x +2 y\right )}{x +y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.326 (sec). Leaf size: 273
dsolve([diff(y(x),x)=2*(2*y(x)-x)/(x+y(x)),y(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{\frac {1}{3}}}{3}+\frac {4 x +\frac {4}{3}}{\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{\frac {1}{3}}}+2 x +\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 82.667 (sec). Leaf size: 122
DSolve[{y'[x]==2*(2*y[x]-x)/(x+y[x]),{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (6 x \left (\frac {2}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+9 x (3 x+4)+8}}+1\right )+\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+9 x (3 x+4)+8}+\frac {4}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+9 x (3 x+4)+8}}+2\right ) \\ \end{align*}