15.20.12 problem 12

Internal problem ID [3320]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:33:27 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 28

dsolve(diff(y(x),x)^3+diff(y(x),x)*x*y(x)=2*y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {x^{3}}{27} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (c_{1} x +1\right )^{2}}{4 c_{1}^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 121.636 (sec). Leaf size: 10682

DSolve[D[y[x],x]^3+D[y[x],x]*x*y[x]==2*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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