80.1.7 problem 16 (b)

Internal problem ID [18537]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 16 (b)
Date solved : Tuesday, January 28, 2025 at 11:54:40 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(v(u),u)+u^2*v(u)=sin(u),v(u), singsol=all)
 

\[ v = \left (\int \sin \left (u \right ) {\mathrm e}^{\frac {u^{3}}{3}}d u +c_{1} \right ) {\mathrm e}^{-\frac {u^{3}}{3}} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 39

DSolve[D[v[u],u]+u^2*v[u]==Sin[u],v[u],u,IncludeSingularSolutions -> True]
 

\[ v(u)\to e^{-\frac {u^3}{3}} \left (\int _1^ue^{\frac {K[1]^3}{3}} \sin (K[1])dK[1]+c_1\right ) \]