36.2.5 problem 5

Internal problem ID [6298]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 5
Date solved : Sunday, March 30, 2025 at 10:49:55 AM
CAS classification : [[_Abel, `2nd type`, `class A`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

Timed Out