88.13.2 problem 2

Internal problem ID [24085]
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 4. Linear equations. Exercises at page 86
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:59:00 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+\frac {3 y}{2}&=x^{4} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(y(x),x)+3/2*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {32 x^{2}}{9}-\frac {16 x^{3}}{9}+\frac {2 x^{4}}{3}-\frac {128 x}{27}+\frac {256}{81}+{\mathrm e}^{-\frac {3 x}{2}} c_1 \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 40

ode=D[y[x],{x,1}]+3/2*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{81} \left (27 x^4-72 x^3+144 x^2-192 x+128\right )+c_1 e^{-3 x/2} \end{align*}

✓ Sympy. Time used: 0.088 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + 3*y(x)/2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {3 x}{2}} + \frac {2 x^{4}}{3} - \frac {16 x^{3}}{9} + \frac {32 x^{2}}{9} - \frac {128 x}{27} + \frac {256}{81} \]