8.4.6 problem 6

Internal problem ID [709]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 6
Date solved : Wednesday, February 05, 2025 at 03:51:20 AM
CAS classification : [_linear]

\begin{align*} y+2 x y^{\prime }&=10 \sqrt {x} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve([y(x)+2*x*diff(y(x),x) = 10*x^(1/2),y(2) = 5],y(x), singsol=all)
 

\[ y = \frac {-10+5 \sqrt {2}+5 x}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 20

DSolve[{y[x]+2*x*D[y[x],x]== 10*x^(1/2),y[2]==5},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 \left (x+\sqrt {2}-2\right )}{\sqrt {x}} \]