80.1.7 problem 16 (b)

Internal problem ID [18466]
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 : Monday, March 31, 2025 at 05:30:11 PM
CAS classification : [_linear]

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

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

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

\[ v = \left (\int \sin \left (u \right ) {\mathrm e}^{\frac {u^{3}}{3}}d u +c_1 \right ) {\mathrm e}^{-\frac {u^{3}}{3}} \]

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

ode=D[v[u],u]+u^2*v[u]==Sin[u]; 
ic={}; 
DSolve[{ode,ic},v[u],u,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 5.862 (sec). Leaf size: 19

from sympy import * 
u = symbols("u") 
v = Function("v") 
ode = Eq(u**2*v(u) - sin(u) + Derivative(v(u), u),0) 
ics = {} 
dsolve(ode,func=v(u),ics=ics)
 

\[ \int \left (u^{2} v{\left (u \right )} - \sin {\left (u \right )}\right ) e^{\frac {u^{3}}{3}}\, du = C_{1} \]