15.21.3 problem 25

Internal problem ID [3327]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:34:14 AM
CAS classification : [[_homogeneous, `class G`], _Clairaut]

\begin{align*} y&=x y^{\prime }-\sqrt {y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 21

dsolve(y(x)=diff(y(x),x)*x-sqrt(diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {1}{4 x} \\ y \left (x \right ) &= c_{1} x -\sqrt {c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 23

DSolve[y[x]==D[y[x],x]*x-Sqrt[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x-\sqrt {c_1} \\ y(x)\to 0 \\ \end{align*}