Internal problem ID [8373]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
\[ \boxed {y^{\prime }+y^{3}+a x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 62
dsolve(diff(y(x),x) + y(x)^3 + a*x*y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 a}{a^{2} x^{2}+2 \operatorname {RootOf}\left (\left (-2 a^{2}\right )^{\frac {1}{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_{1} x +\left (-2 a^{2}\right )^{\frac {1}{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+2 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_{1} +2 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right ) \left (-2 a^{2}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.253 (sec). Leaf size: 195
DSolve[y'[x] + y[x]^3 + a*x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\operatorname {AiryAiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryAi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}{\operatorname {AiryBiPrime}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \operatorname {AiryBi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}+c_1=0,y(x)\right ] \]