Internal problem ID [1655]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\frac {t y}{t^{2}+1}+y^{\prime }-1+\frac {t^{3} y}{t^{4}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (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)
\[ y \relax (t ) = \frac {\int \sqrt {t^{2}+1}\, \left (t^{4}+1\right )^{\frac {1}{4}}d t +c_{1}}{\sqrt {t^{2}+1}\, \left (t^{4}+1\right )^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 21.514 (sec). Leaf size: 55
DSolve[t*y[t]/(t^2+1)+y'[t] == 1-t^3*y[t]/(t^4+1),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} 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}} \\ \end{align*}