8.1.3 problem 3

Internal problem ID [653]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:56:44 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (4\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 11

dsolve([diff(y(x),x) = x^(1/2),y(4) = 0],y(x), singsol=all)
 

\[ y = \frac {2 x^{{3}/{2}}}{3}-\frac {16}{3} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 16

DSolve[{D[y[x],x] == x^(1/2),y[4]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2}{3} \left (x^{3/2}-8\right ) \]