Internal problem ID [13366]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 \sqrt {x}\, y^{\prime }+y=2 x \,{\mathrm e}^{-\sqrt {x}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(2*sqrt(x)*diff(y(x),x)+y(x)=2*x*exp(-sqrt(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 x^{\frac {3}{2}}+3 c_{1} \right ) {\mathrm e}^{-\sqrt {x}}}{3} \]
✓ Solution by Mathematica
Time used: 0.074 (sec). Leaf size: 30
DSolve[2*Sqrt[x]*y'[x]+y[x]==2*x*Exp[-Sqrt[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-\sqrt {x}} \left (2 x^{3/2}+3 c_1\right ) \]