14.1.7 problem 7

Internal problem ID [2478]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:53:45 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: 0.003 (sec). Leaf size: 38

dsolve(diff(y(t),t)+t/(1+t^2)*y(t)=1-t^3/(1+t^4)*y(t),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: 0.989 (sec). Leaf size: 55

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

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