Internal problem ID [3021]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 273.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 182
dsolve(x^2*diff(y(x),x)+a*y(x)^2+b*x^2*y(x)^3 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2^{\frac {1}{3}} a b x}{2 \left (a^{2} b^{2}\right )^{\frac {2}{3}} \RootOf \left (\AiryBi \left (\frac {-b 2^{\frac {2}{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right ) c_{1} \textit {\_Z} +\textit {\_Z} \AiryAi \left (\frac {-b 2^{\frac {2}{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )+\AiryBi \left (1, \frac {-b 2^{\frac {2}{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right ) c_{1}+\AiryAi \left (1, \frac {-b 2^{\frac {2}{3}} x +2 \textit {\_Z}^{2} \left (a^{2} b^{2}\right )^{\frac {1}{3}}}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )\right ) x -2^{\frac {1}{3}} a^{2} b} \]
✓ Solution by Mathematica
Time used: 0.599 (sec). Leaf size: 343
DSolve[x^2 y'[x]+a y[x]^2+b x^2 y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Ai}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\text {Ai}'\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}{\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Bi}\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )+\text {Bi}'\left (\left (\frac {a^{2/3}}{2^{2/3} \sqrt [3]{b} x}+\frac {1}{2^{2/3} \sqrt [3]{b} y(x) \sqrt [3]{a}}\right )^2-\frac {\sqrt [3]{b} x}{\sqrt [3]{2} a^{2/3}}\right )}+c_1=0,y(x)\right ] \]