Internal problem ID [3320]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-c y^{2}=b x +a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 85
dsolve(diff(y(x),x) = a+b*x+c*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\frac {b}{\sqrt {c}}\right )^{\frac {1}{3}} \left (\operatorname {AiryAi}\left (1, -\frac {x b +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (1, -\frac {x b +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )\right )}{\sqrt {c}\, \left (c_{1} \operatorname {AiryAi}\left (-\frac {x b +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )+\operatorname {AiryBi}\left (-\frac {x b +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 143
DSolve[y'[x]==a+b x+c y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {b \left (\operatorname {AiryBiPrime}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )\right )}{(-b c)^{2/3} \left (\operatorname {AiryBi}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )\right )} y(x)\to \frac {b \operatorname {AiryAiPrime}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )}{(-b c)^{2/3} \operatorname {AiryAi}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )} \end{align*}