15.19.23 problem 23

Internal problem ID [3307]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:32:56 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 51

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

\begin{align*} y \left (x \right ) &= -\frac {2 x^{{3}/{2}}}{3} \\ y \left (x \right ) &= \frac {2 x^{{3}/{2}}}{3} \\ y \left (x \right ) &= \frac {4 x^{3}+c_{1}^{2}}{6 c_{1}} \\ y \left (x \right ) &= \frac {c_{1}^{2} x^{3}+4}{6 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.341 (sec). Leaf size: 83

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

\begin{align*} y(x)\to -\frac {1}{6} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to \frac {1}{6} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) \\ y(x)\to -\frac {2 x^{3/2}}{3} \\ y(x)\to \frac {2 x^{3/2}}{3} \\ \end{align*}