58.1.20 problem 20

Internal problem ID [9091]
Book : Second order enumerated odes
Section : section 1
Problem number : 20
Date solved : Monday, January 27, 2025 at 05:37:16 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 18

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

\[ y = \ln \left (\pi \right )+\ln \left (c_{1} \operatorname {AiryAi}\left (x \right )-c_{2} \operatorname {AiryBi}\left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 15

DSolve[D[y[x],{x,2}]+(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log (x-c_1)+c_2 \]