Internal problem ID [5245]
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: 34.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 y-y^{\prime } \left (4-x \right )=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve((1+2*y(x))-(4-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {4 x -\frac {1}{2} x^{2}+c_{1}}{\left (x -4\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 34
DSolve[(1+2*y[x])-(4-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-x^2+8 x+2 c_1}{2 (x-4)^2} y(x)\to -\frac {1}{2} \end{align*}