15.8.27 problem 28

Internal problem ID [3030]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 28
Date solved : Monday, January 27, 2025 at 07:09:30 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y^{\prime }-y+\frac {x^{2}}{y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 70

dsolve(2*x*diff(y(x),x)-y(x)+x^2/y(x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.734 (sec). Leaf size: 80

DSolve[2*x*D[y[x],x]-y[x]+x^2/y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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