88.3.7 problem 7

Internal problem ID [23961]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 22
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:47:52 PM
CAS classification : [_linear]

\begin{align*} 4 y+3 x y^{\prime }&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 44

ode:=3*x*diff(y(x),x)+4*y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 \pi \sqrt {3}}{27 \left (-x \right )^{{4}/{3}} \Gamma \left (\frac {2}{3}\right )}+\frac {{\mathrm e}^{x}}{3 x}-\frac {\Gamma \left (\frac {1}{3}, -x \right )}{9 \left (-x \right )^{{4}/{3}}}+\frac {c_1}{x^{{4}/{3}}} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 32

ode=3*x*D[y[x],x]+4*y[x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\Gamma \left (\frac {4}{3},-x\right )}{3 (-x)^{4/3}}+\frac {c_1}{x^{4/3}} \end{align*}

✓ Sympy. Time used: 1.007 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x) + 4*y(x) - exp(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{\frac {4}{3}}} - \frac {\Gamma \left (\frac {4}{3}, - x\right )}{3 \left (- x\right )^{\frac {4}{3}}} \]