71.4.7 problem 7

Internal problem ID [14379]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:28:47 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 63

dsolve(diff(y(x),x)=x/y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}}}{2} \\ y &= -\frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {\left (12 x^{2}+8 c_{1} \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 79

DSolve[D[y[x],x]==x/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt [3]{-\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ y(x)\to \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ y(x)\to (-1)^{2/3} \sqrt [3]{\frac {3}{2}} \sqrt [3]{x^2+2 c_1} \\ \end{align*}