Internal problem ID [11643]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (u^{2}+1\right ) v^{\prime }+4 v u=3 u} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((u^2+1)*diff(v(u),u)+4*u*v(u)=3*u,v(u), singsol=all)
\[ v \left (u \right ) = \frac {3}{4}+\frac {c_{1}}{\left (u^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 38
DSolve[(u^2+1)*v'[u]+4*u*v[u]==3*u,v[u],u,IncludeSingularSolutions -> True]
\begin{align*} v(u)\to \frac {3 u^4+6 u^2+4 c_1}{4 \left (u^2+1\right )^2} \\ v(u)\to \frac {3}{4} \\ \end{align*}