38.6.8 problem 8

Internal problem ID [8438]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 05:36:46 PM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ y = -\frac {x^{2}}{2}-\frac {x}{2}-\frac {11}{4}+{\mathrm e}^{2 x} c_1 \]

✓ Mathematica. Time used: 0.066 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to e^{2 x} \left (\int _1^xe^{-2 K[1]} \left (K[1]^2+5\right )dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = C_{1} e^{2 x} - \frac {x^{2}}{2} - \frac {x}{2} - \frac {11}{4} \]