44.6.25 problem 25

Internal problem ID [7169]
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 : 25
Date solved : Tuesday, February 04, 2025 at 12:43:40 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

dsolve([diff(y(x),x)=x+5*y(x),y(0) = 3],y(x), singsol=all)
 

\[ y = \frac {76 \,{\mathrm e}^{5 x}}{25}-\frac {x}{5}-\frac {1}{25} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

DSolve[{D[y[x],x]==x+5*y[x],{y[0]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{25} \left (-5 x+76 e^{5 x}-1\right ) \]