73.4.20 problem 5.2 (j)

Internal problem ID [15102]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.2 (j)
Date solved : Tuesday, January 28, 2025 at 07:30:48 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.087 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{3} e^{-\sqrt {x}} \left (2 x^{3/2}+3 c_1\right ) \]