Internal problem ID [10876]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+y^{\prime } y-1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(diff(y(x),x$2)+y(x)*diff(y(x),x)=1,y(x), singsol=all)
\[ \int _{}^{y \left (x \right )}-\frac {2 \,2^{\frac {2}{3}}}{2^{\frac {2}{3}} \textit {\_a}^{2}-4 \operatorname {RootOf}\left (2^{\frac {1}{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_{1} \textit {\_a} +2^{\frac {1}{3}} \textit {\_a} \operatorname {AiryAi}\left (\textit {\_Z} \right )-2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1} -2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right )}d \textit {\_a} -x -c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 73
DSolve[y''[x]+y[x]*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2^{2/3} \left (c_2 \operatorname {AiryAiPrime}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )+\operatorname {AiryBiPrime}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )\right )}{c_2 \operatorname {AiryAi}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )+\operatorname {AiryBi}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )} \\ \end{align*}