44.6.26 problem 26

Internal problem ID [7170]
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 : 26
Date solved : Tuesday, February 04, 2025 at 12:43:42 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=2 x -3 y \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 15

dsolve([diff(y(x),x)=2*x-3*y(x),y(0) = 1/3],y(x), singsol=all)
 

\[ y = \frac {2 x}{3}-\frac {2}{9}+\frac {5 \,{\mathrm e}^{-3 x}}{9} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 21

DSolve[{D[y[x],x]==2*x-3*y[x],{y[0]==1/3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} \left (6 x+5 e^{-3 x}-2\right ) \]