80.4.4 problem 4

Internal problem ID [18555]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:58:45 AM
CAS classification : [_linear]

\begin{align*} p^{\prime }&=\frac {p+a \,t^{3}-2 p t^{2}}{t \left (-t^{2}+1\right )} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(p(t),t)=(p(t)+a*t^3-2*p(t)*t^2 )/(t*(1-t^2)),p(t), singsol=all)
 

\[ p = t \left (\sqrt {t +1}\, \sqrt {t -1}\, c_{1} +a \right ) \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 23

DSolve[D[p[t],t]==(p[t]+a*t^3-2*p[t]*t^2 )/(t*(1-t^2)),p[t],t,IncludeSingularSolutions -> True]
 

\[ p(t)\to t \left (a+c_1 \sqrt {1-t^2}\right ) \]