40.2.10 problem 34

Internal problem ID [6588]
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
Date solved : Monday, January 27, 2025 at 02:14:28 PM
CAS classification : [_separable]

\begin{align*} 1+2 y-\left (4-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.029 (sec). Leaf size: 34

DSolve[(1+2*y[x])-(4-x)*D[y[x],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*}