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 : Monday, January 27, 2025 at 02:41:59 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*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 18

dsolve([diff(y(x),x)=2/10*x^2+y(x),y(0) = 1/2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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