67.2.3 problem Problem 1(c)

Internal problem ID [13960]
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)
Date solved : Tuesday, January 28, 2025 at 08:24:57 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.194 (sec). Leaf size: 60

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

\[ -2 \,2^{{2}/{3}} \left (\int _{}^{y}\frac {1}{2^{{2}/{3}} \textit {\_a}^{2}-4 \operatorname {RootOf}\left (2^{{1}/{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_{1} \textit {\_a} +2^{{1}/{3}} \textit {\_a} \operatorname {AiryAi}\left (\textit {\_Z} \right )-2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1} -2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right )}d \textit {\_a} \right )-x -c_{2} = 0 \]

✓ Solution by Mathematica

Time used: 54.697 (sec). Leaf size: 111

DSolve[D[y[x],{x,2}]+y[x]*D[y[x],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 )} \\ y(x)\to \frac {2^{2/3} \operatorname {AiryAiPrime}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )}{\operatorname {AiryAi}\left (\frac {x-c_1}{\sqrt [3]{2}}\right )} \\ \end{align*}