Internal problem ID [6201]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _exact, _rational]
\[ \boxed {\frac {-x y^{\prime }+y}{\left (x +y\right )^{2}}+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
dsolve((y(x)-x*diff(y(x),x))/(x+y(x))^2+diff(y(x),x)=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {c_{1}}{4}+\frac {1}{4}-\frac {\sqrt {c_{1}^{2}+\left (8 x +2\right ) c_{1} +16 \left (x -\frac {1}{4}\right )^{2}}}{4} \\ y \left (x \right ) &= \frac {c_{1}}{4}+\frac {1}{4}+\frac {\sqrt {c_{1}^{2}+\left (8 x +2\right ) c_{1} +16 \left (x -\frac {1}{4}\right )^{2}}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.468 (sec). Leaf size: 76
DSolve[(y[x]-x*y'[x])/(x+y[x])^2+y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {4 x^2+4 c_1 x+(1+c_1){}^2}+1+c_1\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {4 x^2+4 c_1 x+(1+c_1){}^2}+1+c_1\right ) \\ y(x)\to -x \\ \end{align*}