60.1.571 problem 574

Internal problem ID [10585]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 574
Date solved : Monday, January 27, 2025 at 09:16:49 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} f \left (x -\frac {3 {y^{\prime }}^{2}}{2}\right )+{y^{\prime }}^{3}-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 41

dsolve(f(x-3/2*diff(y(x),x)^2)+diff(y(x),x)^3-y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= f \left (c_{1} \right )-\frac {2 \sqrt {6}\, \sqrt {\left (x -c_{1} \right )^{3}}}{9} \\ y &= f \left (c_{1} \right )+\frac {2 \sqrt {6}\, \sqrt {\left (x -c_{1} \right )^{3}}}{9} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.434 (sec). Leaf size: 62

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

\begin{align*} y(x)\to \frac {1}{9} \left (9 f(c_1)+2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ y(x)\to \frac {1}{9} \left (9 f(c_1)-2 \sqrt {6} (x-c_1){}^{3/2}\right ) \\ \end{align*}