13.2.7 problem 7

Internal problem ID [2305]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:45:06 AM
CAS classification : [_linear]

\begin{align*} \frac {t y}{t^{2}+1}+y^{\prime }&=1-\frac {t^{3} y}{t^{4}+1} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 38

dsolve(t*y(t)/(t^2+1)+diff(y(t),t) = 1-t^3*y(t)/(t^4+1),y(t), singsol=all)
 

\[ y = \frac {\int \left (t^{4}+1\right )^{{1}/{4}} \sqrt {t^{2}+1}d t +c_1}{\left (t^{4}+1\right )^{{1}/{4}} \sqrt {t^{2}+1}} \]

✓ Solution by Mathematica

Time used: 17.895 (sec). Leaf size: 55

DSolve[t*y[t]/(t^2+1)+D[y[t],t] == 1-t^3*y[t]/(t^4+1),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {\int _1^t\sqrt {K[1]^2+1} \sqrt [4]{K[1]^4+1}dK[1]+c_1}{\sqrt {t^2+1} \sqrt [4]{t^4+1}} \]