60.1.13 problem 13

Internal problem ID [10027]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 13
Date solved : Monday, January 27, 2025 at 06:18:42 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 73

dsolve(diff(y(x),x) + y(x)^2 - a*x - b=0,y(x), singsol=all)
 

\[ y = -\frac {i \left (-i a \right )^{{1}/{3}} \left (\operatorname {AiryAi}\left (1, -\frac {a x +b}{\left (-i a \right )^{{2}/{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (1, -\frac {a x +b}{\left (-i a \right )^{{2}/{3}}}\right )\right )}{\operatorname {AiryAi}\left (-\frac {a x +b}{\left (-i a \right )^{{2}/{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {a x +b}{\left (-i a \right )^{{2}/{3}}}\right )} \]

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 105

DSolve[D[y[x],x] + y[x]^2 - a*x - b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{a} \left (\operatorname {AiryBiPrime}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )\right )}{\operatorname {AiryBi}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} \\ y(x)\to \frac {\sqrt [3]{a} \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )}{\operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} \\ \end{align*}