Internal problem ID [6653]
Book: Second order enumerated odes
Section: section 1
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (y^{\prime }\right )^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+diff(y(x),x)^2=x,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (\frac {c_{2} \AiryBi \relax (x )-c_{1} \AiryAi \relax (x )}{\AiryBi \relax (x ) \AiryAi \left (1, x\right )-\AiryAi \relax (x ) \AiryBi \left (1, x\right )}\right ) \]
✓ Solution by Mathematica
Time used: 0.291 (sec). Leaf size: 15
DSolve[y''[x]+(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log (x-c_1)+c_2 \\ \end{align*}