58.1.16 problem 16

Internal problem ID [9087]
Book : Second order enumerated odes
Section : section 1
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:32:24 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} {y^{\prime \prime }}^{2}+y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.195 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)^2+diff(y(x),x)=1,y(x), singsol=all)
 

\begin{align*} y &= x +c_{1} \\ y &= -\frac {1}{12} x^{3}+\frac {1}{2} c_{1} x^{2}-c_{1}^{2} x +x +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 67

DSolve[(D[y[x],{x,2}])^2+D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^3}{12}-\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 \\ y(x)\to -\frac {x^3}{12}+\frac {c_1 x^2}{4}+x-\frac {c_1{}^2 x}{4}+c_2 \\ \end{align*}