84.2.2 problem 1.7

Internal problem ID [22071]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 1. Basic concepts. Supplementary problems
Problem number : 1.7
Date solved : Thursday, October 02, 2025 at 08:23:24 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 47

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

\[ y = \int \left (\int \int \left (\int \frac {{\mathrm e}^{\frac {2 x^{3}-1}{2 x^{2}}}}{x^{4}}d x +c_1 \right ) {\mathrm e}^{\frac {1}{2 x^{2}}}d x d x +c_2 x \right )d x +c_3 x +c_4 \]

✓ Mathematica. Time used: 49.589 (sec). Leaf size: 80

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

\begin{align*} y(x)&\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{\frac {1}{2 K[2]^2}} \left (c_1+\int _1^{K[2]}\frac {e^{K[1]-\frac {1}{2 K[1]^2}}}{K[1]^4}dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \end{align*}

✗ Sympy

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

Timed Out