84.1.1 problem 1.1

Internal problem ID [22065]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts
Problem number : 1.1
Date solved : Thursday, October 02, 2025 at 08:23:20 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-5 x y^{\prime }&=1+{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 78

ode:=diff(diff(diff(y(x),x),x),x)-5*x*diff(y(x),x) = exp(x)+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\int \left (-5^{{2}/{3}} \pi \operatorname {AiryAi}\left (5^{{1}/{3}} x \right ) \int \operatorname {AiryBi}\left (5^{{1}/{3}} x \right ) \left ({\mathrm e}^{x}+1\right )d x +5^{{2}/{3}} \pi \operatorname {AiryBi}\left (5^{{1}/{3}} x \right ) \int \operatorname {AiryAi}\left (5^{{1}/{3}} x \right ) \left ({\mathrm e}^{x}+1\right )d x +5 \operatorname {AiryAi}\left (5^{{1}/{3}} x \right ) c_2 +5 \operatorname {AiryBi}\left (5^{{1}/{3}} x \right ) c_1 \right )d x}{5}+c_3 \]

✓ Mathematica. Time used: 60.805 (sec). Leaf size: 121

ode=D[y[x],{x,3}]-5*x*D[y[x],x]==Exp[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\left (\operatorname {AiryAi}\left (\sqrt [3]{5} K[3]\right ) c_1+\operatorname {AiryBi}\left (\sqrt [3]{5} K[3]\right ) c_2+\operatorname {AiryBi}\left (\sqrt [3]{5} K[3]\right ) \int _1^{K[3]}\frac {\left (1+e^{K[2]}\right ) \pi \operatorname {AiryAi}\left (\sqrt [3]{5} K[2]\right )}{\sqrt [3]{5}}dK[2]+\operatorname {AiryAi}\left (\sqrt [3]{5} K[3]\right ) \int _1^{K[3]}-\frac {\left (1+e^{K[1]}\right ) \pi \operatorname {AiryBi}\left (\sqrt [3]{5} K[1]\right )}{\sqrt [3]{5}}dK[1]\right )dK[3]+c_3 \end{align*}

✓ Sympy. Time used: 0.615 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x*Derivative(y(x), x) - exp(x) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \int \left (C_{2} Ai\left (\sqrt [3]{5} x\right ) + C_{3} Bi\left (\sqrt [3]{5} x\right )\right )\, dx \]