44.4.26 problem 9 (b)

Internal problem ID [7039]
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 (b)
Date solved : Monday, January 27, 2025 at 02:42:01 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{5} \left (-x^2-2 x-2\right )+e^{x-2} \]