38.4.25 problem 9 (a)

Internal problem ID [8324]
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 : Tuesday, September 30, 2025 at 05:26:33 PM
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,op(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: 0.024 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \frac {1}{2} e^x \left (2 \int _0^x\frac {1}{5} e^{-K[1]} K[1]^2dK[1]+1\right ) \end{align*}

✓ Sympy. Time used: 0.083 (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)
 

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