71.8.16 problem 7 (c)

Internal problem ID [14450]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number : 7 (c)
Date solved : Tuesday, January 28, 2025 at 06:31:35 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.034 (sec). Leaf size: 27

dsolve([diff(y(x),x)=-3*x^2/(2*y(x)),y(-1) = 0],y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-x^{3}-1} \\ y &= -\sqrt {-x^{3}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 33

DSolve[{D[y[x],x]==-3*x^2/(2*y[x]),{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^3-1} \\ y(x)\to \sqrt {-x^3-1} \\ \end{align*}