20.2.16 problem Problem 16

Internal problem ID [3608]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 16
Date solved : Monday, January 27, 2025 at 07:47:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {2 \sqrt {y-1}}{3} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

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

\[ y \left (x \right ) = 1 \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 17

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

\[ y(x)\to \frac {1}{36} \left (x^2-2 x+37\right ) \]