Internal problem ID [5237]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary
problems. Page 22
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y+\left (-x^{2}+4\right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve((1+2*y(x))+(4-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = -\frac {1}{2}+\frac {\sqrt {x -2}\, c_{1}}{\sqrt {x +2}} \]
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 35
DSolve[(1+2*y[x])+(4-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2}+\frac {c_1 \sqrt {2-x}}{\sqrt {x+2}} y(x)\to -\frac {1}{2} \end{align*}