Internal problem ID [12315]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {2 x -y}{x +3 y}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve(diff(y(x),x)=(2*x-y(x))/(x+3*y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-\frac {c_{1} x}{3}-\frac {\sqrt {7 c_{1}^{2} x^{2}+3}}{3}}{c_{1}} y \left (x \right ) = \frac {-\frac {c_{1} x}{3}+\frac {\sqrt {7 c_{1}^{2} x^{2}+3}}{3}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.812 (sec). Leaf size: 114
DSolve[y'[x]==(2*x-y[x])/(x+3*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (-x-\sqrt {7 x^2+3 e^{2 c_1}}\right ) y(x)\to \frac {1}{3} \left (-x+\sqrt {7 x^2+3 e^{2 c_1}}\right ) y(x)\to \frac {1}{3} \left (-\sqrt {7} \sqrt {x^2}-x\right ) y(x)\to \frac {1}{3} \left (\sqrt {7} \sqrt {x^2}-x\right ) \end{align*}