40.2.2 problem 25

Internal problem ID [6580]
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
Date solved : Monday, January 27, 2025 at 02:14:04 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.087 (sec). Leaf size: 87

DSolve[(1+2*y[x])+(4-x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt {2-x} \left (\sqrt {4-x^2}-2 \sqrt {x+2}+2 c_1 \left (x+2 \sqrt {2-x}-2\right )\right )}{2 \sqrt {x+2} \left (x+2 \sqrt {2-x}-2\right )} \\ y(x)\to -\frac {1}{2} \\ \end{align*}