79.1.14 problem 3 (ii)

Internal problem ID [18501]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 3 (ii)
Date solved : Tuesday, January 28, 2025 at 11:51:10 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve((1+2*x(t))+(4-t^2)*diff(x(t),t)=0,x(t), singsol=all)
 

\[ x = -\frac {1}{2}+\frac {\sqrt {t -2}\, c_{1}}{\sqrt {t +2}} \]

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 87

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

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