64.5.6 problem 6

Internal problem ID [13319]
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
Date solved : Tuesday, January 28, 2025 at 05:22:04 AM
CAS classification : [_separable]

\begin{align*} \left (u^{2}+1\right ) v^{\prime }+4 v u&=3 u \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.045 (sec). Leaf size: 38

DSolve[(u^2+1)*D[ v[u],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*}