Internal problem ID [7727]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 147.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+y^{3} x^{2} a +b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 178
dsolve(x^2*diff(y(x),x) + a*x^2*y(x)^3 + b*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2^{\frac {1}{3}} a b x}{2^{\frac {1}{3}} a \,b^{2}-2 \left (a^{2} b^{2}\right )^{\frac {2}{3}} \RootOf \left (\AiryBi \left (-\frac {a 2^{\frac {2}{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \AiryAi \left (-\frac {a 2^{\frac {2}{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )+\AiryBi \left (1, -\frac {a 2^{\frac {2}{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right ) c_{1}+\AiryAi \left (1, -\frac {a 2^{\frac {2}{3}} x -2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )\right ) x} \]
✓ Solution by Mathematica
Time used: 0.602 (sec). Leaf size: 343
DSolve[x^2*y'[x] + a*x^2*y[x]^3 + b*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\frac {\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {Ai}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\operatorname {Ai}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}{\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \operatorname {Bi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\operatorname {Bi}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}+c_1=0,y(x)\right ] \]