44.6.8 problem 8

Internal problem ID [7152]
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 : 8
Date solved : Tuesday, February 04, 2025 at 12:40:22 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x)=2*y(x)+x^2+5,y(x), singsol=all)
 

\[ y = c_1 \,{\mathrm e}^{2 x}-\frac {x^{2}}{2}-\frac {x}{2}-\frac {11}{4} \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 28

DSolve[D[y[x],x]==2*y[x]+x^2+5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (-2 x^2-2 x+4 c_1 e^{2 x}-11\right ) \]