15.20.1 problem 1

Internal problem ID [3309]
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 : 1
Date solved : Monday, January 27, 2025 at 07:33:06 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 40

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

\begin{align*} y \left (x \right ) &= \frac {\left (-4 x -1\right ) \sqrt {4 x +1}}{12}-\frac {x}{2}+c_{1} \\ y \left (x \right ) &= -\frac {x}{2}+\frac {\left (4 x +1\right )^{{3}/{2}}}{12}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 54

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

\begin{align*} y(x)\to \frac {1}{2} \left (-\frac {1}{6} (4 x+1)^{3/2}-x\right )+c_1 \\ y(x)\to \frac {1}{12} \left ((4 x+1)^{3/2}-6 x+12 c_1\right ) \\ \end{align*}