85.1.1 problem 1 (a)

Internal problem ID [22406]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 08:38:24 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x^{2}+5 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(x),x) = x^2+5*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x^{2}}{5}-\frac {2 x}{25}-\frac {2}{125}+{\mathrm e}^{5 x} c_1 \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 29

ode=D[y[x],{x,1}]==x^2+5*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^2}{5}-\frac {2 x}{25}+c_1 e^{5 x}-\frac {2}{125} \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - 5*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{5 x} - \frac {x^{2}}{5} - \frac {2 x}{25} - \frac {2}{125} \]