73.3.7 problem 4.3 (g)

Internal problem ID [15041]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.3 (g)
Date solved : Tuesday, January 28, 2025 at 07:28:20 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&=x^{2} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x)+4*y(x)=x^2,y(x), singsol=all)
 

\[ y = \frac {x^{2}}{4}-\frac {x}{8}+\frac {1}{32}+c_{1} {\mathrm e}^{-4 x} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 32

DSolve[D[y[x],x]+4*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-4 x} \left (\int _1^xe^{4 K[1]} K[1]^2dK[1]+c_1\right ) \]