71.8.15 problem 7 (b)

Internal problem ID [14449]
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 (b)
Date solved : Tuesday, January 28, 2025 at 06:31:31 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 )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 15

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

\[ y = \frac {\sqrt {-4 x^{3}-3}}{2} \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 20

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

\[ y(x)\to \frac {1}{2} \sqrt {-4 x^3-3} \]