44.4.25 problem 9 (a)

Internal problem ID [7038]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 9 (a)
Date solved : Sunday, March 30, 2025 at 11:36:02 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 18

ode:=diff(y(x),x) = 1/5*x^2+y(x); 
ic:=y(0) = 1/2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {x^{2}}{5}-\frac {2 x}{5}-\frac {2}{5}+\frac {9 \,{\mathrm e}^{x}}{10} \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 25

ode=D[y[x],x]==2/10*x^2+y[x]; 
ic={y[0]==1/2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{10} \left (9 e^x-2 \left (x^2+2 x+2\right )\right ) \]

✓ Sympy. Time used: 0.180 (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 = {y(0): 1/2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x^{2}}{5} - \frac {2 x}{5} + \frac {9 e^{x}}{10} - \frac {2}{5} \]