30.2.2 problem 2

Internal problem ID [7430]
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 : 2
Date solved : Tuesday, September 30, 2025 at 04:32:40 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{\prime }+x t&={\mathrm e}^{x} \end{align*}

✗ Maple

ode:=diff(x(t),t)+x(t)*t = exp(x(t)); 
dsolve(ode,x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],t]+x[t]*t==Exp[x[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*x(t) - exp(x(t)) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : The given ODE t*x(t) - exp(x(t)) + Derivative(x(t), t) cannot be solved by the lie group method