35.2.11 problem 11

Internal problem ID [6103]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 11
Date solved : Monday, January 27, 2025 at 01:36:15 PM
CAS classification : [_quadrature]

\begin{align*} 2 y^{\prime }&=3 \left (y-2\right )^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 9

dsolve([2*diff(y(x),x)=3*(y(x)-2)^(1/3),y(1) = 3],y(x), singsol=all)
 

\[ y = 2+x^{{3}/{2}} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 12

DSolve[{2*D[y[x],x]==3*(y[x]-2)^(1/3),{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^{3/2}+2 \]