73.9.5 problem 14.1 (e)

Internal problem ID [15266]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (e)
Date solved : Tuesday, January 28, 2025 at 07:51:10 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+3 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 28

dsolve(x*diff(y(x),x)+3*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (2 x^{2}-2 x +1\right ) {\mathrm e}^{2 x}+4 c_{1}}{4 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 30

DSolve[x*D[y[x],x]+3*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^xe^{2 K[1]} K[1]^2dK[1]+c_1}{x^3} \]