20.4.16 problem Problem 25

Internal problem ID [3651]
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
Date solved : Monday, January 27, 2025 at 07:50:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {4 y-2 x}{x +y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.555 (sec). Leaf size: 72

dsolve([diff(y(x),x)=2*(2*y(x)-x)/(x+y(x)),y(0) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{{1}/{3}}}{3}+\frac {4 x +\frac {4}{3}}{\left (3 \sqrt {3}\, x \sqrt {x \left (27 x +8\right )}+27 x^{2}+36 x +8\right )^{{1}/{3}}}+2 x +\frac {2}{3} \]

✓ Solution by Mathematica

Time used: 60.269 (sec). Leaf size: 121

DSolve[{D[y[x],x]==2*(2*y[x]-x)/(x+y[x]),{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} \left (x \left (\frac {12}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}}+6\right )+\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}+\frac {4}{\sqrt [3]{3 \sqrt {3} \sqrt {x^3 (27 x+8)}+27 x^2+36 x+8}}+2\right ) \]